Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers
Abstract
:1. Introduction
2. The Structural Model
3. Statistical Properties of
3.1. Expected Value
3.2. Variance
3.3. Integrated Relative Mean Squared Error
4. Numerical Results
4.1. The Dependent Counting Geometric INAR(1) Model
4.2. Estimation of the Bispectrum
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A
- 1.
- Simulation for DCGINAR(1)function [xt] = simdcg12(a,th,n,m,L)xt(1)=round(m); h=random(’unif’,0,1,[n,1]);for i=1:nif h(i)et(i)=0;elseifet(i)=random(’geo’,m/(1+m));elseet(i)=random(’geo’,(m*(a+th-2*a*th)/(1+m*(a+th-2*a*th))));end endh=random(’unif’,0,1,[n,1]);for t=2:nfor i=1:xt(t-1)if h(i)<=aaxt=random(’bin’,xt(t-1),a+th-a*th,[n,1]);elseaxt=random(’bin’,xt(t-1),a*(1-th),[n,1]);end endxt(t)=axt(t)+et(t); xt(t-1)=xt(t);endfor j=1:Lfor i=1:tX(:,i,j)=xt(j*mm-mm+i);end end end
- 2.
- Function to calculatefunction [Im]=multi(t,K,Np,X)ja=0;r=;[w1,w2]= meshgrid(0:/20:,0:20:);// mention here danill function onlyto clarificationfor i=1:tAI=(i)/t;CI=AI*pi;h(1,i,2)=sin(CI)/CI;endfor k=1:3 for l=1:3 for m=1:3qq=0;for i=1:tqq=qq+(h(:,i,k)*h(:,i,l)*h(:,i,m));Q(k,l,m)=qq;endja=ja+end end endfor j=1:L for j2=1:(Np+1) for j1=j2:(Np+1)result=0;for k=1:K for l=1:K for m=1:Ktap1=0;tap2=0;tap3=0;for i=1:ttap1=tap1+sum(h(:,i,k)*X(:,i,j)*exp(-r*j1*i));tap2=tap2+sum(h(:,i,l)*X(:,i,j)*exp(-r*j2*i));tap3=tap3+sum(h(:,i,m)*X(:,i,j)*exp(r*(j1+j2)*i));endQ(k,l,m); result=result+Q(k,l,m)*tap1*tap2*tap3;end end endIm(j1,j2,j)=result;end end end end
- 3.
- Function to calculatefunction [fsmooth]=fhatsmooth(NP,,Im)mu(1)=0;syms lamd1; syms lamd2;NP1=NP+1; mu(NP1)=1; NP3=2*NP+1;for I=2:NP3mu(I)=(I-1)./NP;endfor j=1:L for i1=1:NP1 for i2=i1:NP1I1=(mu(i1)-lamd1)/();I2=(mu(i2)-lamd2)/();I3=(mu(i1)+mu(i2)-lamd1-lamd2)/();ker1=(sin (I1)/I1); ker2=(sin (I2)/I2);ker3=(sin (I3)/I3); mker=ker1*ker2*ker3;Kernel=mker/((2*pi));mkImu= Kernel*Im(j);fjsmooth(i1,i2,j)=integral2(mkImu,-,,-,);end end endfsmooth=sum(fjsmooth)/();end
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0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 11.2352 | 9.9030 | 7.2167 | 4.8711 | 3.2912 | 2.3014 | 1.6801 | 1.2790 | 1.0108 | 0.8254 | 0.6933 | 0.5969 | 0.5252 | 0.4712 | 0.4302 | 0.3991 | 0.3759 | 0.3590 | 0.3476 | 0.3410 | 0.3388 | |
0.05 | 9.9030 | 7.9364 | 5.5644 | 3.7554 | 2.5791 | 1.8410 | 1.3712 | 1.0627 | 0.8530 | 0.7060 | 0.6001 | 0.5220 | 0.4636 | 0.4194 | 0.3859 | 0.3607 | 0.3421 | 0.3289 | 0.3205 | 0.3164 | 0.3164 | |
0.10 | 7.2167 | 5.5644 | 3.8987 | 2.6715 | 1.8703 | 1.3599 | 1.0296 | 0.8093 | 0.6577 | 0.5502 | 0.4721 | 0.4142 | 0.3708 | 0.3379 | 0.3130 | 0.2945 | 0.2811 | 0.2720 | 0.2667 | 0.2650 | 0.2667 | |
0.15 | 4.8711 | 3.7554 | 2.6715 | 1.8651 | 1.3289 | 0.9812 | 0.7527 | 0.5984 | 0.4911 | 0.4145 | 0.3585 | 0.3168 | 0.2855 | 0.2619 | 0.2442 | 0.2312 | 0.2220 | 0.2161 | 0.2133 | 0.2133 | 0.2161 | |
0.20 | 3.2912 | 2.5791 | 1.8703 | 1.3289 | 0.9612 | 0.7188 | 0.5574 | 0.4473 | 0.3701 | 0.3147 | 0.2741 | 0.2438 | 0.2211 | 0.2041 | 0.1914 | 0.1823 | 0.1761 | 0.1725 | 0.1714 | 0.1725 | 0.1761 | |
0.25 | 2.3014 | 1.8410 | 1.3599 | 0.9812 | 0.7188 | 0.5432 | 0.4251 | 0.3438 | 0.2866 | 0.2453 | 0.2150 | 0.1924 | 0.1755 | 0.1629 | 0.1537 | 0.1473 | 0.1432 | 0.1412 | 0.1412 | 0.1432 | 0.1473 | |
0.30 | 1.6801 | 1.3712 | 1.0296 | 0.7527 | 0.5574 | 0.4251 | 0.3352 | 0.2731 | 0.2291 | 0.1973 | 0.1739 | 0.1566 | 0.1437 | 0.1342 | 0.1274 | 0.1228 | 0.1201 | 0.1193 | 0.1201 | 0.1228 | 0.1274 | |
0.35 | 1.2790 | 1.0627 | 0.8093 | 0.5984 | 0.4473 | 0.3438 | 0.2731 | 0.2239 | 0.1890 | 0.1637 | 0.1452 | 0.1314 | 0.1213 | 0.1140 | 0.1088 | 0.1056 | 0.1040 | 0.1040 | 0.1056 | 0.1088 | 0.1140 | |
0.40 | 1.0108 | 0.8530 | 0.6577 | 0.4911 | 0.3701 | 0.2866 | 0.2291 | 0.1890 | 0.1604 | 0.1398 | 0.1247 | 0.1135 | 0.1054 | 0.0996 | 0.0958 | 0.0935 | 0.0928 | 0.0935 | 0.0958 | 0.0996 | 0.1054 | |
0.45 | 0.8254 | 0.7060 | 0.5502 | 0.4145 | 0.3147 | 0.2453 | 0.1973 | 0.1637 | 0.1398 | 0.1225 | 0.1099 | 0.1007 | 0.0940 | 0.0894 | 0.0866 | 0.0852 | 0.0852 | 0.0866 | 0.0894 | 0.0940 | 0.1007 | |
0.50 | 0.6933 | 0.6001 | 0.4721 | 0.3585 | 0.2741 | 0.2150 | 0.1739 | 0.1452 | 0.1247 | 0.1099 | 0.0991 | 0.0914 | 0.0859 | 0.0823 | 0.0802 | 0.0795 | 0.0802 | 0.0823 | 0.0859 | 0.0914 | 0.0991 | |
0.55 | 0.5969 | 0.5220 | 0.4142 | 0.3168 | 0.2438 | 0.1924 | 0.1566 | 0.1314 | 0.1135 | 0.1007 | 0.0914 | 0.0848 | 0.0802 | 0.0774 | 0.0760 | 0.0760 | 0.0774 | 0.0802 | 0.0848 | 0.0914 | 0.1007 | |
0.60 | 0.5252 | 0.4636 | 0.3708 | 0.2855 | 0.2211 | 0.1755 | 0.1437 | 0.1213 | 0.1054 | 0.0940 | 0.0859 | 0.0802 | 0.0765 | 0.0744 | 0.0737 | 0.0744 | 0.0765 | 0.0802 | 0.0859 | 0.0940 | 0.1054 | |
0.65 | 0.4712 | 0.4194 | 0.3379 | 0.2619 | 0.2041 | 0.1629 | 0.1342 | 0.1140 | 0.0996 | 0.0894 | 0.0823 | 0.0774 | 0.0744 | 0.0729 | 0.0729 | 0.0744 | 0.0774 | 0.0823 | 0.0894 | 0.0996 | 0.1140 | |
0.70 | 0.4302 | 0.3859 | 0.3130 | 0.2442 | 0.1914 | 0.1537 | 0.1274 | 0.1088 | 0.0958 | 0.0866 | 0.0802 | 0.0760 | 0.0737 | 0.0729 | 0.0737 | 0.0760 | 0.0802 | 0.0866 | 0.0958 | 0.1088 | 0.1274 | |
0.75 | 0.3991 | 0.3607 | 0.2945 | 0.2312 | 0.1823 | 0.1473 | 0.1228 | 0.1056 | 0.0935 | 0.0852 | 0.0795 | 0.0760 | 0.0744 | 0.0744 | 0.0760 | 0.0795 | 0.0852 | 0.0935 | 0.1056 | 0.1228 | 0.1473 | |
0.80 | 0.3759 | 0.3421 | 0.2811 | 0.2220 | 0.1761 | 0.1432 | 0.1201 | 0.1040 | 0.0928 | 0.0852 | 0.0802 | 0.0774 | 0.0765 | 0.0774 | 0.0802 | 0.0852 | 0.0928 | 0.1040 | 0.1201 | 0.1432 | 0.1761 | |
0.85 | 0.3590 | 0.3289 | 0.2720 | 0.2161 | 0.1725 | 0.1412 | 0.1193 | 0.1040 | 0.0935 | 0.0866 | 0.0823 | 0.0802 | 0.0802 | 0.0823 | 0.0866 | 0.0935 | 0.1040 | 0.1193 | 0.1412 | 0.1725 | 0.2161 | |
0.90 | 0.3476 | 0.3205 | 0.2667 | 0.2133 | 0.1714 | 0.1412 | 0.1201 | 0.1056 | 0.0958 | 0.0894 | 0.0859 | 0.0848 | 0.0859 | 0.0894 | 0.0958 | 0.1056 | 0.1201 | 0.1412 | 0.1714 | 0.2133 | 0.2667 | |
0.95 | 0.3410 | 0.3164 | 0.2650 | 0.2133 | 0.1725 | 0.1432 | 0.1228 | 0.1088 | 0.0996 | 0.0940 | 0.0914 | 0.0914 | 0.0940 | 0.0996 | 0.1088 | 0.1228 | 0.1432 | 0.1725 | 0.2133 | 0.2650 | 0.3164 | |
0.3388 | 0.3164 | 0.2667 | 0.2161 | 0.1761 | 0.1473 | 0.1274 | 0.1140 | 0.1054 | 0.1007 | 0.0991 | 0.1007 | 0.1054 | 0.1140 | 0.1274 | 0.1473 | 0.1761 | 0.2161 | 0.2667 | 0.3164 | 0.3388 |
0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 11.5611 | 9.8639 | 6.805 | 5.275 | 5.0508 | 4.3963 | 3.2455 | 2.5186 | 2.1825 | 1.7485 | 1.2759 | 0.899 | 0.4956 | 0.1455 | 0.031 | 0.0523 | 0.1327 | 0.3934 | 0.7266 | 0.8635 | 0.8596 | |
0.05 | 9.8639 | 7.5674 | 5.5329 | 4.7663 | 4.3513 | 3.4883 | 2.6402 | 2.1651 | 1.804 | 1.3793 | 0.989 | 0.6164 | 0.248 | 0.0617 | 0.0367 | 0.0764 | 0.2108 | 0.4938 | 0.7315 | 0.7956 | 0.7956 | |
0.10 | 6.805 | 5.5329 | 4.4949 | 3.6911 | 3.1039 | 2.5518 | 2.041 | 1.6091 | 1.2796 | 0.9615 | 0.6098 | 0.2774 | 0.0947 | 0.0663 | 0.0486 | 0.1093 | 0.238 | 0.447 | 0.6061 | 0.6621 | 0.6061 | |
0.15 | 5.275 | 4.7663 | 3.6911 | 2.7918 | 2.4084 | 2.0923 | 1.6085 | 1.2101 | 0.946 | 0.6288 | 0.291 | 0.1124 | 0.1078 | 0.0936 | 0.074 | 0.1313 | 0.2286 | 0.3926 | 0.5349 | 0.5349 | 0.3926 | |
0.20 | 5.0508 | 4.3513 | 3.1039 | 2.4084 | 2.1953 | 1.8327 | 1.3443 | 0.9943 | 0.6876 | 0.3333 | 0.1309 | 0.1422 | 0.1689 | 0.158 | 0.0986 | 0.14 | 0.2229 | 0.3851 | 0.4803 | 0.3851 | 0.2229 | |
0.25 | 4.3963 | 3.4883 | 2.5518 | 2.0923 | 1.8327 | 1.4598 | 1.0525 | 0.6889 | 0.3474 | 0.1427 | 0.1584 | 0.2125 | 0.2723 | 0.2004 | 0.1002 | 0.1297 | 0.2081 | 0.3296 | 0.3296 | 0.2081 | 0.1297 | |
0.30 | 3.2455 | 2.6402 | 2.041 | 1.6085 | 1.3443 | 1.0525 | 0.6715 | 0.3207 | 0.1371 | 0.1593 | 0.2179 | 0.315 | 0.3177 | 0.1877 | 0.0858 | 0.1116 | 0.1642 | 0.2084 | 0.1642 | 0.1116 | 0.0858 | |
0.35 | 2.5186 | 2.1651 | 1.6091 | 1.2101 | 0.9943 | 0.6889 | 0.3207 | 0.1299 | 0.1565 | 0.2244 | 0.3306 | 0.3767 | 0.3048 | 0.1649 | 0.0759 | 0.0905 | 0.1066 | 0.1066 | 0.0905 | 0.0759 | 0.1649 | |
0.40 | 2.1825 | 1.804 | 1.2796 | 0.946 | 0.6876 | 0.3474 | 0.1371 | 0.1565 | 0.2331 | 0.3603 | 0.4181 | 0.3822 | 0.2832 | 0.1539 | 0.065 | 0.0621 | 0.0575 | 0.0621 | 0.065 | 0.1539 | 0.2832 | |
0.45 | 1.7485 | 1.3793 | 0.9615 | 0.6288 | 0.3333 | 0.1427 | 0.1593 | 0.2244 | 0.3603 | 0.4384 | 0.4081 | 0.3417 | 0.2543 | 0.1264 | 0.0427 | 0.032 | 0.032 | 0.0427 | 0.1264 | 0.2543 | 0.3417 | |
0.50 | 1.2759 | 0.989 | 0.6098 | 0.291 | 0.1309 | 0.1584 | 0.2179 | 0.3306 | 0.4181 | 0.4081 | 0.348 | 0.2927 | 0.1993 | 0.0795 | 0.0212 | 0.0172 | 0.0212 | 0.0795 | 0.1993 | 0.2927 | 0.348 | |
0.55 | 0.899 | 0.6164 | 0.2774 | 0.1124 | 0.1422 | 0.2125 | 0.315 | 0.3767 | 0.3822 | 0.3417 | 0.2927 | 0.2252 | 0.123 | 0.0387 | 0.0112 | 0.0112 | 0.0387 | 0.123 | 0.2252 | 0.2927 | 0.3417 | |
0.60 | 0.4956 | 0.248 | 0.0947 | 0.1078 | 0.1689 | 0.2723 | 0.3177 | 0.3048 | 0.2832 | 0.2543 | 0.1993 | 0.123 | 0.053 | 0.018 | 0.0063 | 0.018 | 0.053 | 0.123 | 0.1993 | 0.2543 | 0.2832 | |
0.65 | 0.1455 | 0.0617 | 0.0663 | 0.0936 | 0.158 | 0.2004 | 0.1877 | 0.1649 | 0.1539 | 0.1264 | 0.0795 | 0.0387 | 0.018 | 0.0075 | 0.0075 | 0.018 | 0.0387 | 0.0795 | 0.1264 | 0.1539 | 0.1649 | |
0.70 | 0.031 | 0.0367 | 0.0486 | 0.074 | 0.0986 | 0.1002 | 0.0858 | 0.0759 | 0.065 | 0.0427 | 0.0212 | 0.0112 | 0.0063 | 0.0075 | 0.0063 | 0.0112 | 0.0212 | 0.0427 | 0.065 | 0.0759 | 0.0858 | |
0.75 | 0.0523 | 0.0764 | 0.1093 | 0.1313 | 0.14 | 0.1297 | 0.1116 | 0.0905 | 0.0621 | 0.032 | 0.0172 | 0.0112 | 0.018 | 0.018 | 0.0112 | 0.0172 | 0.032 | 0.0621 | 0.0905 | 0.1116 | 0.1297 | |
0.80 | 0.1327 | 0.2108 | 0.238 | 0.2286 | 0.2229 | 0.2081 | 0.1642 | 0.1066 | 0.0575 | 0.032 | 0.0212 | 0.0387 | 0.053 | 0.0387 | 0.0212 | 0.032 | 0.0575 | 0.1066 | 0.1642 | 0.2081 | 0.2229 | |
0.85 | 0.3934 | 0.4938 | 0.447 | 0.3926 | 0.3851 | 0.3296 | 0.2084 | 0.1066 | 0.0621 | 0.0427 | 0.0795 | 0.123 | 0.123 | 0.0795 | 0.0427 | 0.0621 | 0.1066 | 0.2084 | 0.3296 | 0.3851 | 0.3926 | |
0.90 | 0.7266 | 0.7315 | 0.6061 | 0.5349 | 0.4803 | 0.3296 | 0.1642 | 0.0905 | 0.065 | 0.1264 | 0.1993 | 0.2252 | 0.1993 | 0.1264 | 0.065 | 0.0905 | 0.1642 | 0.3296 | 0.4803 | 0.5349 | 0.6061 | |
0.95 | 0.8635 | 0.7956 | 0.6621 | 0.5349 | 0.3851 | 0.2081 | 0.1116 | 0.0759 | 0.1539 | 0.2543 | 0.2927 | 0.2927 | 0.2543 | 0.1539 | 0.0759 | 0.1116 | 0.2081 | 0.3851 | 0.5349 | 0.6621 | 0.7956 | |
0.8596 | 0.7956 | 0.6061 | 0.3926 | 0.2229 | 0.1297 | 0.0858 | 0.1649 | 0.2832 | 0.3417 | 0.348 | 0.3417 | 0.2832 | 0.1649 | 0.0858 | 0.1297 | 0.2229 | 0.3926 | 0.6061 | 0.7956 | 0.8596 |
0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 11.8543 | 9.8299 | 6.4759 | 5.1308 | 4.8888 | 4.0414 | 3.1227 | 2.6088 | 2.0355 | 1.5383 | 1.3358 | 0.973 | 0.4167 | 0.1198 | 0.0449 | 0.0224 | 0.1698 | 0.4111 | 0.6113 | 0.8491 | 0.992 | |
0.05 | 9.8299 | 7.265 | 5.2475 | 4.5589 | 4.0463 | 3.2341 | 2.5984 | 2.0978 | 1.6109 | 1.3051 | 1.038 | 0.5797 | 0.2031 | 0.0663 | 0.0285 | 0.056 | 0.2405 | 0.4563 | 0.6559 | 0.8357 | 0.8357 | |
0.10 | 6.4759 | 5.2475 | 4.1552 | 3.3621 | 2.8863 | 2.3991 | 1.8622 | 1.4797 | 1.2184 | 0.904 | 0.5513 | 0.252 | 0.1004 | 0.0379 | 0.0641 | 0.0708 | 0.2379 | 0.4365 | 0.5755 | 0.6275 | 0.5755 | |
0.15 | 5.1308 | 4.5589 | 3.3621 | 2.6317 | 2.3501 | 1.8867 | 1.4409 | 1.2279 | 0.926 | 0.5266 | 0.2631 | 0.1371 | 0.0633 | 0.0934 | 0.0888 | 0.0769 | 0.2497 | 0.4201 | 0.4738 | 0.4738 | 0.4201 | |
0.20 | 4.8888 | 4.0463 | 2.8863 | 2.3501 | 2.0266 | 1.6006 | 1.3111 | 1.0234 | 0.5913 | 0.275 | 0.1567 | 0.0944 | 0.1708 | 0.1419 | 0.1057 | 0.0882 | 0.2636 | 0.3792 | 0.392 | 0.3792 | 0.2636 | |
0.25 | 4.0414 | 3.2341 | 2.3991 | 1.8867 | 1.6006 | 1.3558 | 1.0176 | 0.6087 | 0.2874 | 0.1524 | 0.1007 | 0.2373 | 0.2416 | 0.1576 | 0.1133 | 0.0867 | 0.2216 | 0.2922 | 0.2922 | 0.2216 | 0.0867 | |
0.30 | 3.1227 | 2.5984 | 1.8622 | 1.4409 | 1.3111 | 1.0176 | 0.5854 | 0.2866 | 0.1543 | 0.095 | 0.2442 | 0.3242 | 0.259 | 0.1633 | 0.1076 | 0.0707 | 0.1652 | 0.2107 | 0.1652 | 0.0707 | 0.1076 | |
0.35 | 2.6088 | 2.0978 | 1.4797 | 1.2279 | 1.0234 | 0.6087 | 0.2866 | 0.1601 | 0.0997 | 0.2396 | 0.347 | 0.3613 | 0.279 | 0.1612 | 0.091 | 0.0547 | 0.124 | 0.124 | 0.0547 | 0.091 | 0.1612 | |
0.40 | 2.0355 | 1.6109 | 1.2184 | 0.926 | 0.5913 | 0.2874 | 0.1543 | 0.0997 | 0.2437 | 0.3294 | 0.3742 | 0.3766 | 0.2664 | 0.1319 | 0.0682 | 0.0395 | 0.0704 | 0.0395 | 0.0682 | 0.1319 | 0.2664 | |
0.45 | 1.5383 | 1.3051 | 0.904 | 0.5266 | 0.275 | 0.1524 | 0.095 | 0.2396 | 0.3294 | 0.3493 | 0.3836 | 0.3539 | 0.2143 | 0.0974 | 0.0487 | 0.0221 | 0.0221 | 0.0487 | 0.0974 | 0.2143 | 0.3539 | |
0.50 | 1.3358 | 1.038 | 0.5513 | 0.2631 | 0.1567 | 0.1007 | 0.2442 | 0.347 | 0.3742 | 0.3836 | 0.3862 | 0.3049 | 0.1694 | 0.0744 | 0.0292 | 0.0075 | 0.0292 | 0.0744 | 0.1694 | 0.3049 | 0.3862 | |
0.55 | 0.973 | 0.5797 | 0.252 | 0.1371 | 0.0944 | 0.2373 | 0.3242 | 0.3613 | 0.3766 | 0.3539 | 0.3049 | 0.2209 | 0.1185 | 0.0408 | 0.009 | 0.009 | 0.0408 | 0.1185 | 0.2209 | 0.3049 | 0.3539 | |
0.60 | 0.4167 | 0.2031 | 0.1004 | 0.0633 | 0.1708 | 0.2416 | 0.259 | 0.279 | 0.2664 | 0.2143 | 0.1694 | 0.1185 | 0.0498 | 0.0097 | 0.0084 | 0.0097 | 0.0498 | 0.1185 | 0.1694 | 0.2143 | 0.2664 | |
0.65 | 0.1198 | 0.0663 | 0.0379 | 0.0934 | 0.1419 | 0.1576 | 0.1633 | 0.1612 | 0.1319 | 0.0974 | 0.0744 | 0.0408 | 0.0097 | 0.0072 | 0.0072 | 0.0097 | 0.0408 | 0.0744 | 0.0974 | 0.1319 | 0.1612 | |
0.70 | 0.0449 | 0.0285 | 0.0641 | 0.0888 | 0.1057 | 0.1133 | 0.1076 | 0.091 | 0.0682 | 0.0487 | 0.0292 | 0.009 | 0.0084 | 0.0072 | 0.0084 | 0.009 | 0.0292 | 0.0487 | 0.0682 | 0.091 | 0.1076 | |
0.75 | 0.0224 | 0.056 | 0.0708 | 0.0769 | 0.0882 | 0.0867 | 0.0707 | 0.0547 | 0.0395 | 0.0221 | 0.0075 | 0.009 | 0.0097 | 0.0097 | 0.009 | 0.0075 | 0.0221 | 0.0395 | 0.0547 | 0.0707 | 0.0867 | |
0.80 | 0.1698 | 0.2405 | 0.2379 | 0.2497 | 0.2636 | 0.2216 | 0.1652 | 0.124 | 0.0704 | 0.0221 | 0.0292 | 0.0408 | 0.0498 | 0.0408 | 0.0292 | 0.0221 | 0.0704 | 0.124 | 0.1652 | 0.2216 | 0.2636 | |
0.85 | 0.4111 | 0.4563 | 0.4365 | 0.4201 | 0.3792 | 0.2922 | 0.2107 | 0.124 | 0.0395 | 0.0487 | 0.0744 | 0.1185 | 0.1185 | 0.0744 | 0.0487 | 0.0395 | 0.124 | 0.2107 | 0.2922 | 0.3792 | 0.4201 | |
0.90 | 0.6113 | 0.6559 | 0.5755 | 0.4738 | 0.392 | 0.2922 | 0.1652 | 0.0547 | 0.0682 | 0.0974 | 0.1694 | 0.2209 | 0.1694 | 0.0974 | 0.0682 | 0.0547 | 0.1652 | 0.2922 | 0.392 | 0.4738 | 0.5755 | |
0.95 | 0.8491 | 0.8357 | 0.6275 | 0.4738 | 0.3792 | 0.2216 | 0.0707 | 0.091 | 0.1319 | 0.2143 | 0.3049 | 0.3049 | 0.2143 | 0.1319 | 0.091 | 0.0707 | 0.2216 | 0.3792 | 0.4738 | 0.6275 | 0.8357 | |
0.992 | 0.8357 | 0.5755 | 0.4201 | 0.2636 | 0.0867 | 0.1076 | 0.1612 | 0.2664 | 0.3539 | 0.3862 | 0.3539 | 0.2664 | 0.1612 | 0.1076 | 0.0867 | 0.2636 | 0.4201 | 0.5755 | 0.8357 | 0.992 |
0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 12.1855 | 9.7818 | 6.1558 | 5.0108 | 4.6472 | 3.7593 | 3.1864 | 2.5834 | 1.7753 | 1.535 | 1.43 | 0.8699 | 0.3765 | 0.1561 | 0.0212 | 0.0401 | 0.1436 | 0.3453 | 0.6957 | 0.8756 | 0.8651 | |
0.05 | 9.7818 | 6.9518 | 4.9739 | 4.3212 | 3.7435 | 3.1001 | 2.5697 | 1.9182 | 1.4788 | 1.3272 | 0.9991 | 0.5125 | 0.2168 | 0.0514 | 0.0261 | 0.0678 | 0.1993 | 0.439 | 0.6992 | 0.7797 | 0.7797 | |
0.10 | 6.1558 | 4.9739 | 3.797 | 3.0813 | 2.7342 | 2.214 | 1.6891 | 1.4148 | 1.1323 | 0.821 | 0.5214 | 0.2614 | 0.0633 | 0.056 | 0.0392 | 0.0833 | 0.2245 | 0.3907 | 0.5512 | 0.6223 | 0.5512 | |
0.15 | 5.0108 | 4.3212 | 3.0813 | 2.5621 | 2.2229 | 1.6558 | 1.4176 | 1.2327 | 0.7966 | 0.4873 | 0.303 | 0.087 | 0.0785 | 0.0955 | 0.0548 | 0.107 | 0.2274 | 0.3502 | 0.5004 | 0.5004 | 0.3502 | |
0.20 | 4.6472 | 3.7435 | 2.7342 | 2.2229 | 1.7738 | 1.4826 | 1.3182 | 0.9256 | 0.5041 | 0.302 | 0.1075 | 0.1151 | 0.1432 | 0.1431 | 0.075 | 0.1156 | 0.2172 | 0.3393 | 0.4296 | 0.3393 | 0.2172 | |
0.25 | 3.7593 | 3.1001 | 2.214 | 1.6558 | 1.4826 | 1.2874 | 0.9246 | 0.5472 | 0.2917 | 0.1001 | 0.1327 | 0.1961 | 0.2002 | 0.1827 | 0.0756 | 0.1031 | 0.1965 | 0.2721 | 0.2721 | 0.1965 | 0.1031 | |
0.30 | 3.1864 | 2.5697 | 1.6891 | 1.4176 | 1.3182 | 0.9246 | 0.5601 | 0.3246 | 0.0991 | 0.1265 | 0.2312 | 0.2802 | 0.2613 | 0.1884 | 0.0692 | 0.0956 | 0.1615 | 0.1766 | 0.1615 | 0.0956 | 0.0692 | |
0.35 | 2.5834 | 1.9182 | 1.4148 | 1.2327 | 0.9256 | 0.5472 | 0.3246 | 0.1078 | 0.1227 | 0.2157 | 0.3233 | 0.3581 | 0.2639 | 0.1688 | 0.0627 | 0.0768 | 0.1023 | 0.1023 | 0.0768 | 0.0627 | 0.1688 | |
0.40 | 1.7753 | 1.4788 | 1.1323 | 0.7966 | 0.5041 | 0.2917 | 0.0991 | 0.1227 | 0.1926 | 0.2778 | 0.3807 | 0.3331 | 0.2178 | 0.141 | 0.0463 | 0.0448 | 0.0545 | 0.0448 | 0.0463 | 0.141 | 0.2178 | |
0.45 | 1.535 | 1.3272 | 0.821 | 0.4873 | 0.302 | 0.1001 | 0.1265 | 0.2157 | 0.2778 | 0.3667 | 0.397 | 0.3079 | 0.2037 | 0.1168 | 0.0303 | 0.0269 | 0.0269 | 0.0303 | 0.1168 | 0.2037 | 0.3079 | |
0.50 | 1.43 | 0.9991 | 0.5214 | 0.303 | 0.1075 | 0.1327 | 0.2312 | 0.3233 | 0.3807 | 0.397 | 0.3808 | 0.2989 | 0.1752 | 0.0794 | 0.0189 | 0.0138 | 0.0189 | 0.0794 | 0.1752 | 0.2989 | 0.3808 | |
0.55 | 0.8699 | 0.5125 | 0.2614 | 0.087 | 0.1151 | 0.1961 | 0.2802 | 0.3581 | 0.3331 | 0.3079 | 0.2989 | 0.2078 | 0.0963 | 0.04 | 0.0078 | 0.0078 | 0.04 | 0.0963 | 0.2078 | 0.2989 | 0.3079 | |
0.60 | 0.3765 | 0.2168 | 0.0633 | 0.0785 | 0.1432 | 0.2002 | 0.2613 | 0.2639 | 0.2178 | 0.2037 | 0.1752 | 0.0963 | 0.0409 | 0.0138 | 0.0037 | 0.0138 | 0.0409 | 0.0963 | 0.1752 | 0.2037 | 0.2178 | |
0.65 | 0.1561 | 0.0514 | 0.056 | 0.0955 | 0.1431 | 0.1827 | 0.1884 | 0.1688 | 0.141 | 0.1168 | 0.0794 | 0.04 | 0.0138 | 0.0065 | 0.0065 | 0.0138 | 0.04 | 0.0794 | 0.1168 | 0.141 | 0.1688 | |
0.70 | 0.0212 | 0.0261 | 0.0392 | 0.0548 | 0.075 | 0.0756 | 0.0692 | 0.0627 | 0.0463 | 0.0303 | 0.0189 | 0.0078 | 0.0037 | 0.0065 | 0.0037 | 0.0078 | 0.0189 | 0.0303 | 0.0463 | 0.0627 | 0.0692 | |
0.75 | 0.0401 | 0.0678 | 0.0833 | 0.107 | 0.1156 | 0.1031 | 0.0956 | 0.0768 | 0.0448 | 0.0269 | 0.0138 | 0.0078 | 0.0138 | 0.0138 | 0.0078 | 0.0138 | 0.0269 | 0.0448 | 0.0768 | 0.0956 | 0.1031 | |
0.80 | 0.1436 | 0.1993 | 0.2245 | 0.2274 | 0.2172 | 0.1965 | 0.1615 | 0.1023 | 0.0545 | 0.0269 | 0.0189 | 0.04 | 0.0409 | 0.04 | 0.0189 | 0.0269 | 0.0545 | 0.1023 | 0.1615 | 0.1965 | 0.2172 | |
0.85 | 0.3453 | 0.439 | 0.3907 | 0.3502 | 0.3393 | 0.2721 | 0.1766 | 0.1023 | 0.0448 | 0.0303 | 0.0794 | 0.0963 | 0.0963 | 0.0794 | 0.0303 | 0.0448 | 0.1023 | 0.1766 | 0.2721 | 0.3393 | 0.3502 | |
0.90 | 0.6957 | 0.6992 | 0.5512 | 0.5004 | 0.4296 | 0.2721 | 0.1615 | 0.0768 | 0.0463 | 0.1168 | 0.1752 | 0.2078 | 0.1752 | 0.1168 | 0.0463 | 0.0768 | 0.1615 | 0.2721 | 0.4296 | 0.5004 | 0.5512 | |
0.95 | 0.8756 | 0.7797 | 0.6223 | 0.5004 | 0.3393 | 0.1965 | 0.0956 | 0.0627 | 0.141 | 0.2037 | 0.2989 | 0.2989 | 0.2037 | 0.141 | 0.0627 | 0.0956 | 0.1965 | 0.3393 | 0.5004 | 0.6223 | 0.7797 | |
0.8651 | 0.7797 | 0.5512 | 0.3502 | 0.2172 | 0.1031 | 0.0692 | 0.1688 | 0.2178 | 0.3079 | 0.3808 | 0.3079 | 0.2178 | 0.1688 | 0.0692 | 0.1031 | 0.2172 | 0.3502 | 0.5512 | 0.7797 | 0.8651 |
0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 12.5334 | 9.7103 | 5.8637 | 4.8954 | 4.3392 | 3.6252 | 3.307 | 2.3805 | 1.6303 | 1.6359 | 1.3316 | 0.8026 | 0.443 | 0.1251 | 0.0185 | 0.0278 | 0.1274 | 0.4105 | 0.6202 | 0.8232 | 0.9779 | |
0.05 | 9.7103 | 6.6408 | 4.7131 | 4.0541 | 3.4897 | 3.0468 | 2.4689 | 1.7336 | 1.4372 | 1.2988 | 0.9097 | 0.5245 | 0.207 | 0.0422 | 0.0197 | 0.0522 | 0.2012 | 0.444 | 0.6288 | 0.7897 | 0.7897 | |
0.10 | 5.8637 | 4.7131 | 3.4449 | 2.8787 | 2.5907 | 2.0082 | 1.5874 | 1.3495 | 1.0073 | 0.7834 | 0.5252 | 0.2164 | 0.0619 | 0.0401 | 0.033 | 0.073 | 0.1921 | 0.3975 | 0.5326 | 0.5629 | 0.5326 | |
0.15 | 4.8954 | 4.0541 | 2.8787 | 2.5156 | 2.0091 | 1.5184 | 1.4537 | 1.1125 | 0.7144 | 0.5323 | 0.2551 | 0.076 | 0.0689 | 0.0789 | 0.0542 | 0.0819 | 0.2023 | 0.396 | 0.4463 | 0.4463 | 0.396 | |
0.20 | 4.3392 | 3.4897 | 2.5907 | 2.0091 | 1.564 | 1.4323 | 1.2347 | 0.8125 | 0.4997 | 0.2662 | 0.0919 | 0.0875 | 0.1397 | 0.1334 | 0.0628 | 0.0885 | 0.2076 | 0.3419 | 0.3644 | 0.3419 | 0.2076 | |
0.25 | 3.6252 | 3.0468 | 2.0082 | 1.5184 | 1.4323 | 1.1815 | 0.8759 | 0.5519 | 0.2427 | 0.0933 | 0.1031 | 0.1719 | 0.229 | 0.1497 | 0.0661 | 0.0883 | 0.1742 | 0.2711 | 0.2711 | 0.1742 | 0.0883 | |
0.30 | 3.307 | 2.4689 | 1.5874 | 1.4537 | 1.2347 | 0.8759 | 0.6219 | 0.2803 | 0.0891 | 0.1091 | 0.2115 | 0.2944 | 0.2687 | 0.1648 | 0.0688 | 0.0775 | 0.1443 | 0.2109 | 0.1443 | 0.0775 | 0.0688 | |
0.35 | 2.3805 | 1.7336 | 1.3495 | 1.1125 | 0.8125 | 0.5519 | 0.2803 | 0.0912 | 0.0924 | 0.1989 | 0.3222 | 0.3072 | 0.2631 | 0.1524 | 0.0536 | 0.0569 | 0.0996 | 0.0996 | 0.0569 | 0.0536 | 0.1524 | |
0.40 | 1.6303 | 1.4372 | 1.0073 | 0.7144 | 0.4997 | 0.2427 | 0.0891 | 0.0924 | 0.1643 | 0.2954 | 0.3277 | 0.2931 | 0.2372 | 0.1157 | 0.0385 | 0.0384 | 0.0459 | 0.0384 | 0.0385 | 0.1157 | 0.2372 | |
0.45 | 1.6359 | 1.2988 | 0.7834 | 0.5323 | 0.2662 | 0.0933 | 0.1091 | 0.1989 | 0.2954 | 0.3637 | 0.3782 | 0.3199 | 0.218 | 0.1006 | 0.0314 | 0.0214 | 0.0214 | 0.0314 | 0.1006 | 0.218 | 0.3199 | |
0.50 | 1.3316 | 0.9097 | 0.5252 | 0.2551 | 0.0919 | 0.1031 | 0.2115 | 0.3222 | 0.3277 | 0.3782 | 0.3719 | 0.2649 | 0.1708 | 0.0738 | 0.0158 | 0.0089 | 0.0158 | 0.0738 | 0.1708 | 0.2649 | 0.3719 | |
0.55 | 0.8026 | 0.5245 | 0.2164 | 0.076 | 0.0875 | 0.1719 | 0.2944 | 0.3072 | 0.2931 | 0.3199 | 0.2649 | 0.1786 | 0.1078 | 0.0319 | 0.0057 | 0.0057 | 0.0319 | 0.1078 | 0.1786 | 0.2649 | 0.3199 | |
0.60 | 0.443 | 0.207 | 0.0619 | 0.0689 | 0.1397 | 0.229 | 0.2687 | 0.2631 | 0.2372 | 0.218 | 0.1708 | 0.1078 | 0.0446 | 0.0111 | 0.0034 | 0.0111 | 0.0446 | 0.1078 | 0.1708 | 0.218 | 0.2372 | |
0.65 | 0.1251 | 0.0422 | 0.0401 | 0.0789 | 0.1334 | 0.1497 | 0.1648 | 0.1524 | 0.1157 | 0.1006 | 0.0738 | 0.0319 | 0.0111 | 0.0048 | 0.0048 | 0.0111 | 0.0319 | 0.0738 | 0.1006 | 0.1157 | 0.1524 | |
0.70 | 0.0185 | 0.0197 | 0.033 | 0.0542 | 0.0628 | 0.0661 | 0.0688 | 0.0536 | 0.0385 | 0.0314 | 0.0158 | 0.0057 | 0.0034 | 0.0048 | 0.0034 | 0.0057 | 0.0158 | 0.0314 | 0.0385 | 0.0536 | 0.0688 | |
0.75 | 0.0278 | 0.0522 | 0.073 | 0.0819 | 0.0885 | 0.0883 | 0.0775 | 0.0569 | 0.0384 | 0.0214 | 0.0089 | 0.0057 | 0.0111 | 0.0111 | 0.0057 | 0.0089 | 0.0214 | 0.0384 | 0.0569 | 0.0775 | 0.0883 | |
0.80 | 0.1274 | 0.2012 | 0.1921 | 0.2023 | 0.2076 | 0.1742 | 0.1443 | 0.0996 | 0.0459 | 0.0214 | 0.0158 | 0.0319 | 0.0446 | 0.0319 | 0.0158 | 0.0214 | 0.0459 | 0.0996 | 0.1443 | 0.1742 | 0.2076 | |
0.85 | 0.4105 | 0.444 | 0.3975 | 0.396 | 0.3419 | 0.2711 | 0.2109 | 0.0996 | 0.0384 | 0.0314 | 0.0738 | 0.1078 | 0.1078 | 0.0738 | 0.0314 | 0.0384 | 0.0996 | 0.2109 | 0.2711 | 0.3419 | 0.396 | |
0.90 | 0.6202 | 0.6288 | 0.5326 | 0.4463 | 0.3644 | 0.2711 | 0.1443 | 0.0569 | 0.0385 | 0.1006 | 0.1708 | 0.1786 | 0.1708 | 0.1006 | 0.0385 | 0.0569 | 0.1443 | 0.2711 | 0.3644 | 0.4463 | 0.5326 | |
0.99 | 0.8232 | 0.7897 | 0.5629 | 0.4463 | 0.3419 | 0.1742 | 0.0775 | 0.0536 | 0.1157 | 0.218 | 0.2649 | 0.2649 | 0.218 | 0.1157 | 0.0536 | 0.0775 | 0.1742 | 0.3419 | 0.4463 | 0.5629 | 0.7897 | |
0.9779 | 0.7897 | 0.5326 | 0.396 | 0.2076 | 0.0883 | 0.0688 | 0.1524 | 0.2372 | 0.3199 | 0.3719 | 0.3199 | 0.2372 | 0.1524 | 0.0688 | 0.0883 | 0.2076 | 0.396 | 0.5326 | 0.7897 | 0.9779 |
0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 13.4644 | 9.6273 | 5.5741 | 5.0625 | 3.9013 | 3.7343 | 3.5292 | 2.003 | 1.7797 | 1.6493 | 1.1196 | 1.0007 | 0.4267 | 0.0763 | 0.0502 | 0.0193 | 0.1917 | 0.278 | 0.7085 | 0.947 | 0.7685 | |
0.05 | 9.6273 | 6.1914 | 4.4866 | 3.7537 | 3.2252 | 3.0682 | 2.2472 | 1.5952 | 1.4472 | 1.1478 | 0.8941 | 0.5519 | 0.1516 | 0.0514 | 0.0259 | 0.0507 | 0.1942 | 0.3745 | 0.692 | 0.7207 | 0.7207 | |
0.10 | 5.5741 | 4.4866 | 2.9923 | 2.7953 | 2.3867 | 1.7578 | 1.6121 | 1.168 | 0.9068 | 0.8263 | 0.4439 | 0.1775 | 0.0935 | 0.0246 | 0.0627 | 0.0463 | 0.2367 | 0.3297 | 0.4741 | 0.6092 | 0.4741 | |
0.15 | 5.0625 | 3.7537 | 2.7953 | 2.5937 | 1.7123 | 1.5801 | 1.4795 | 0.9168 | 0.8186 | 0.5145 | 0.1783 | 0.137 | 0.0551 | 0.0732 | 0.0715 | 0.0713 | 0.2614 | 0.2826 | 0.5023 | 0.5023 | 0.2826 | |
0.20 | 3.9013 | 3.2252 | 2.3867 | 1.7123 | 1.4155 | 1.3354 | 1.0688 | 0.7609 | 0.4689 | 0.1893 | 0.1262 | 0.0743 | 0.1537 | 0.078 | 0.1006 | 0.0722 | 0.2055 | 0.2752 | 0.3813 | 0.2752 | 0.2055 | |
0.25 | 3.7343 | 3.0682 | 1.7578 | 1.5801 | 1.3354 | 1.0764 | 0.9894 | 0.4865 | 0.1936 | 0.1505 | 0.0769 | 0.2295 | 0.1811 | 0.1219 | 0.114 | 0.0635 | 0.2239 | 0.2335 | 0.2335 | 0.2239 | 0.0635 | |
0.30 | 3.5292 | 2.2472 | 1.6121 | 1.4795 | 1.0688 | 0.9894 | 0.6283 | 0.1991 | 0.1524 | 0.0905 | 0.2362 | 0.269 | 0.2814 | 0.1366 | 0.0995 | 0.0689 | 0.1886 | 0.1419 | 0.1886 | 0.0689 | 0.0995 | |
0.35 | 2.003 | 1.5952 | 1.168 | 0.9168 | 0.7609 | 0.4865 | 0.1991 | 0.1211 | 0.071 | 0.2164 | 0.2152 | 0.3246 | 0.2451 | 0.0931 | 0.0834 | 0.0447 | 0.0884 | 0.0884 | 0.0447 | 0.0834 | 0.0931 | |
0.40 | 1.7797 | 1.4472 | 0.9068 | 0.8186 | 0.4689 | 0.1936 | 0.1524 | 0.071 | 0.2116 | 0.2455 | 0.3235 | 0.3532 | 0.2079 | 0.0972 | 0.0682 | 0.0264 | 0.0697 | 0.0264 | 0.0682 | 0.0972 | 0.2079 | |
0.45 | 1.6493 | 1.1478 | 0.8263 | 0.5145 | 0.1893 | 0.1505 | 0.0905 | 0.2164 | 0.2455 | 0.3778 | 0.36 | 0.3065 | 0.2221 | 0.081 | 0.0407 | 0.0213 | 0.0213 | 0.0407 | 0.081 | 0.2221 | 0.3065 | |
0.50 | 1.1196 | 0.8941 | 0.4439 | 0.1783 | 0.1262 | 0.0769 | 0.2362 | 0.2152 | 0.3235 | 0.36 | 0.2678 | 0.2804 | 0.1584 | 0.042 | 0.028 | 0.0054 | 0.028 | 0.042 | 0.1584 | 0.2804 | 0.2678 | |
0.55 | 1.0007 | 0.5519 | 0.1775 | 0.137 | 0.0743 | 0.2295 | 0.269 | 0.3246 | 0.3532 | 0.3065 | 0.2804 | 0.229 | 0.0937 | 0.0327 | 0.0084 | 0.0084 | 0.0327 | 0.0937 | 0.229 | 0.2804 | 0.3065 | |
0.60 | 0.4267 | 0.1516 | 0.0935 | 0.0551 | 0.1537 | 0.1811 | 0.2814 | 0.2451 | 0.2079 | 0.2221 | 0.1584 | 0.0937 | 0.0507 | 0.0067 | 0.009 | 0.0067 | 0.0507 | 0.0937 | 0.1584 | 0.2221 | 0.2079 | |
0.65 | 0.0763 | 0.0514 | 0.0246 | 0.0732 | 0.078 | 0.1219 | 0.1366 | 0.0931 | 0.0972 | 0.081 | 0.042 | 0.0327 | 0.0067 | 0.0045 | 0.0045 | 0.0067 | 0.0327 | 0.042 | 0.081 | 0.0972 | 0.0931 | |
0.70 | 0.0502 | 0.0259 | 0.0627 | 0.0715 | 0.1006 | 0.114 | 0.0995 | 0.0834 | 0.0682 | 0.0407 | 0.028 | 0.0084 | 0.009 | 0.0045 | 0.009 | 0.0084 | 0.028 | 0.0407 | 0.0682 | 0.0834 | 0.0995 | |
0.75 | 0.0193 | 0.0507 | 0.0463 | 0.0713 | 0.0722 | 0.0635 | 0.0689 | 0.0447 | 0.0264 | 0.0213 | 0.0054 | 0.0084 | 0.0067 | 0.0067 | 0.0084 | 0.0054 | 0.0213 | 0.0264 | 0.0447 | 0.0689 | 0.0635 | |
0.80 | 0.1917 | 0.1942 | 0.2367 | 0.2614 | 0.2055 | 0.2239 | 0.1886 | 0.0884 | 0.0697 | 0.0213 | 0.028 | 0.0327 | 0.0507 | 0.0327 | 0.028 | 0.0213 | 0.0697 | 0.0884 | 0.1886 | 0.2239 | 0.2055 | |
0.85 | 0.278 | 0.3745 | 0.3297 | 0.2826 | 0.2752 | 0.2335 | 0.1419 | 0.0884 | 0.0264 | 0.0407 | 0.042 | 0.0937 | 0.0937 | 0.042 | 0.0407 | 0.0264 | 0.0884 | 0.1419 | 0.2335 | 0.2752 | 0.2826 | |
0.90 | 0.7085 | 0.692 | 0.4741 | 0.5023 | 0.3813 | 0.2335 | 0.1886 | 0.0447 | 0.0682 | 0.081 | 0.1584 | 0.229 | 0.1584 | 0.081 | 0.0682 | 0.0447 | 0.1886 | 0.2335 | 0.3813 | 0.5023 | 0.4741 | |
0.95 | 0.947 | 0.7207 | 0.6092 | 0.5023 | 0.2752 | 0.2239 | 0.0689 | 0.0834 | 0.0972 | 0.2221 | 0.2804 | 0.2804 | 0.2221 | 0.0972 | 0.0834 | 0.0689 | 0.2239 | 0.2752 | 0.5023 | 0.6092 | 0.7207 | |
0.7685 | 0.7207 | 0.4741 | 0.2826 | 0.2055 | 0.0635 | 0.0995 | 0.0931 | 0.2079 | 0.3065 | 0.2678 | 0.3065 | 0.2079 | 0.0931 | 0.0995 | 0.0635 | 0.2055 | 0.2826 | 0.4741 | 0.7207 | 0.7685 |
0 | 0.05 | 0.10 | 0.15 | 0.20 | 0.25 | 0.30 | 0.35 | 0.40 | 0.45 | 0.50 | 0.55 | 0.60 | 0.65 | 0.70 | 0.75 | 0.80 | 0.85 | 0.90 | 0.95 | |||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
0 | 14.2824 | 9.4763 | 5.4075 | 5.0651 | 3.498 | 4.0708 | 3.3823 | 1.836 | 1.9688 | 1.3601 | 1.2737 | 1.0541 | 0.2942 | 0.1474 | 0.0148 | 0.0474 | 0.0954 | 0.3983 | 0.6718 | 0.7916 | 0.9987 | |
0.05 | 9.4763 | 5.8259 | 4.2558 | 3.4236 | 3.0709 | 3.0204 | 2.028 | 1.5466 | 1.331 | 1.0707 | 0.9431 | 0.453 | 0.1685 | 0.0374 | 0.0213 | 0.0542 | 0.1584 | 0.4211 | 0.5937 | 0.7241 | 0.7241 | |
0.10 | 5.4075 | 4.2558 | 2.6673 | 2.7929 | 2.1147 | 1.6808 | 1.5871 | 0.9697 | 0.9737 | 0.7364 | 0.376 | 0.2422 | 0.04 | 0.0511 | 0.023 | 0.0842 | 0.1557 | 0.3452 | 0.5039 | 0.4866 | 0.5039 | |
0.15 | 5.0651 | 3.4236 | 2.7929 | 2.4658 | 1.5057 | 1.6863 | 1.2762 | 0.9095 | 0.8585 | 0.3755 | 0.2576 | 0.0739 | 0.0697 | 0.07 | 0.0452 | 0.106 | 0.163 | 0.3756 | 0.4337 | 0.4337 | 0.3756 | |
0.20 | 3.498 | 3.0709 | 2.1147 | 1.5057 | 1.296 | 1.1638 | 1.0254 | 0.688 | 0.3758 | 0.2199 | 0.0672 | 0.1099 | 0.083 | 0.1195 | 0.0489 | 0.095 | 0.1524 | 0.2778 | 0.3318 | 0.2778 | 0.1524 | |
0.25 | 4.0708 | 3.0204 | 1.6808 | 1.6863 | 1.1638 | 1.2155 | 1.008 | 0.392 | 0.2875 | 0.0751 | 0.1302 | 0.1687 | 0.1824 | 0.1669 | 0.0573 | 0.1157 | 0.1466 | 0.2762 | 0.2762 | 0.1466 | 0.1157 | |
0.30 | 3.3823 | 2.028 | 1.5871 | 1.2762 | 1.0254 | 1.008 | 0.4845 | 0.2522 | 0.0825 | 0.1228 | 0.1692 | 0.3153 | 0.2161 | 0.1657 | 0.0585 | 0.0937 | 0.1227 | 0.1939 | 0.1227 | 0.0937 | 0.0585 | |
0.35 | 1.836 | 1.5466 | 0.9697 | 0.9095 | 0.688 | 0.392 | 0.2522 | 0.0583 | 0.1089 | 0.1291 | 0.2551 | 0.3013 | 0.1731 | 0.1368 | 0.0386 | 0.0635 | 0.0698 | 0.0698 | 0.0635 | 0.0386 | 0.1368 | |
0.40 | 1.9688 | 1.331 | 0.9737 | 0.8585 | 0.3758 | 0.2875 | 0.0825 | 0.1089 | 0.1602 | 0.273 | 0.3426 | 0.3388 | 0.2007 | 0.1263 | 0.0366 | 0.051 | 0.0352 | 0.051 | 0.0366 | 0.1263 | 0.2007 | |
0.45 | 1.3601 | 1.0707 | 0.7364 | 0.3755 | 0.2199 | 0.0751 | 0.1228 | 0.1291 | 0.273 | 0.2949 | 0.3099 | 0.3163 | 0.149 | 0.0968 | 0.0234 | 0.0205 | 0.0205 | 0.0234 | 0.0968 | 0.149 | 0.3163 | |
0.50 | 1.2737 | 0.9431 | 0.376 | 0.2576 | 0.0672 | 0.1302 | 0.1692 | 0.2551 | 0.3426 | 0.3099 | 0.3363 | 0.2725 | 0.1327 | 0.072 | 0.0111 | 0.0141 | 0.0111 | 0.072 | 0.1327 | 0.2725 | 0.3363 | |
0.55 | 1.0541 | 0.453 | 0.2422 | 0.0739 | 0.1099 | 0.1687 | 0.3153 | 0.3013 | 0.3388 | 0.3163 | 0.2725 | 0.2284 | 0.0928 | 0.0321 | 0.0071 | 0.0071 | 0.0321 | 0.0928 | 0.2284 | 0.2725 | 0.3163 | |
0.60 | 0.2942 | 0.1685 | 0.04 | 0.0697 | 0.083 | 0.1824 | 0.2161 | 0.1731 | 0.2007 | 0.149 | 0.1327 | 0.0928 | 0.0241 | 0.0119 | 0.0021 | 0.0119 | 0.0241 | 0.0928 | 0.1327 | 0.149 | 0.2007 | |
0.65 | 0.1474 | 0.0374 | 0.0511 | 0.07 | 0.1195 | 0.1669 | 0.1657 | 0.1368 | 0.1263 | 0.0968 | 0.072 | 0.0321 | 0.0119 | 0.0048 | 0.0048 | 0.0119 | 0.0321 | 0.072 | 0.0968 | 0.1263 | 0.1368 | |
0.70 | 0.0148 | 0.0213 | 0.023 | 0.0452 | 0.0489 | 0.0573 | 0.0585 | 0.0386 | 0.0366 | 0.0234 | 0.0111 | 0.0071 | 0.0021 | 0.0048 | 0.0021 | 0.0071 | 0.0111 | 0.0234 | 0.0366 | 0.0386 | 0.0585 | |
0.75 | 0.0474 | 0.0542 | 0.0842 | 0.106 | 0.095 | 0.1157 | 0.0937 | 0.0635 | 0.051 | 0.0205 | 0.0141 | 0.0071 | 0.0119 | 0.0119 | 0.0071 | 0.0141 | 0.0205 | 0.051 | 0.0635 | 0.0937 | 0.1157 | |
0.80 | 0.0954 | 0.1584 | 0.1557 | 0.163 | 0.1524 | 0.1466 | 0.1227 | 0.0698 | 0.0352 | 0.0205 | 0.0111 | 0.0321 | 0.0241 | 0.0321 | 0.0111 | 0.0205 | 0.0352 | 0.0698 | 0.1227 | 0.1466 | 0.1524 | |
0.85 | 0.3983 | 0.4211 | 0.3452 | 0.3756 | 0.2778 | 0.2762 | 0.1939 | 0.0698 | 0.051 | 0.0234 | 0.072 | 0.0928 | 0.0928 | 0.072 | 0.0234 | 0.051 | 0.0698 | 0.1939 | 0.2762 | 0.2778 | 0.3756 | |
0.90 | 0.6718 | 0.5937 | 0.5039 | 0.4337 | 0.3318 | 0.2762 | 0.1227 | 0.0635 | 0.0366 | 0.0968 | 0.1327 | 0.2284 | 0.1327 | 0.0968 | 0.0366 | 0.0635 | 0.1227 | 0.2762 | 0.3318 | 0.4337 | 0.5039 | |
0.95 | 0.7916 | 0.7241 | 0.4866 | 0.4337 | 0.2778 | 0.1466 | 0.0937 | 0.0386 | 0.1263 | 0.149 | 0.2725 | 0.2725 | 0.149 | 0.1263 | 0.0386 | 0.0937 | 0.1466 | 0.2778 | 0.4337 | 0.4866 | 0.7241 | |
0.9987 | 0.7241 | 0.5039 | 0.3756 | 0.1524 | 0.1157 | 0.0585 | 0.1368 | 0.2007 | 0.3163 | 0.3363 | 0.3163 | 0.2007 | 0.1368 | 0.0585 | 0.1157 | 0.1524 | 0.3756 | 0.5039 | 0.7241 | 0.9987 |
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El-Morshedy, M.; Teamah, A.E.-M.A.M.; El-Menshawy, M.H.; EL-Sagheer, R.M.; Faied, H.M.; Al-Bossly, A.; Eliwa, M.S. Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers. Mathematics 2022, 10, 3284. https://doi.org/10.3390/math10183284
El-Morshedy M, Teamah AE-MAM, El-Menshawy MH, EL-Sagheer RM, Faied HM, Al-Bossly A, Eliwa MS. Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers. Mathematics. 2022; 10(18):3284. https://doi.org/10.3390/math10183284
Chicago/Turabian StyleEl-Morshedy, Mahmoud, Abd El-Moneim A. M. Teamah, Mohammed H. El-Menshawy, Rashad M. EL-Sagheer, Hasnaa M. Faied, Afrah Al-Bossly, and Mohamed S. Eliwa. 2022. "Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers" Mathematics 10, no. 18: 3284. https://doi.org/10.3390/math10183284
APA StyleEl-Morshedy, M., Teamah, A. E.-M. A. M., El-Menshawy, M. H., EL-Sagheer, R. M., Faied, H. M., Al-Bossly, A., & Eliwa, M. S. (2022). Some Asymptotic Properties of a Kernel Bispectum Estimate with Different Multitapers. Mathematics, 10(18), 3284. https://doi.org/10.3390/math10183284