Search Results (2)

This paper presents a new bivariate mixture Lindley power function (BMLPF) distribution that employs a conditional approach with non-identical asymmetric distributions, distinguishing itself by the incorporation of a functional shape parameter. Various structural properties of bivariate distribution are presented, including explicit marginals, cumulative distribution function (CDF), product moments, correlation coefficients, conditional densities, moment generating functions, conditional mean, and variances. The parameters of the proposed distribution are evaluated using the maximum likelihood estimation method. To assess the effectiveness of this estimation approach, an extensive simulation study is carried out. The analysis quantifies these point estimators with their standard errors, RMSE, LCL, and UCL. This research significantly contributes to the development and application of bivariate distributions particularly in modeling and analyzing various types of data. Full article

This study introduces a flexible model with two parameters by combining the type II half-logistic-G family with the inverted Topp–Leone distribution. The proposed model is referred to as the half logistic inverted Topp–Leone (HLITL) distribution. The associated probability density function can be considered a mixture of the inverted Topp–Leone distributions. The proposed model can be deemed an acceptable model for fitting the right-skewed, reversed J-shaped, and unimodal data. The statistical properties, including the moments, Bonferroni and Lorenz curves, Rényi entropy, and quantile function, are derived. Additionally, the plots of the skewness and kurtosis measures are plotted based on the quantiles. The parameter estimators are implemented using the maximum likelihood method based on two sampling schemes: the simple random sample method and the ranked set sampling method. The proposed method is evaluated by using simulations. The results show that the maximum likelihood estimates of the parameters under ranked set sampling are more accurate than those under simple random sampling. Generally, there is good agreement between the theoretical and empirical results. Two real datasets are used to compare the HLITL model with the following models: alpha power exponential, alpha power Lindley, odd Fréchet inverse exponential, and odd Fréchet inverse Rayleigh models. The comparison results show that the HLITL model represents a better alternative lifetime distribution than the other competitive distributions. Full article