Search Results (57)

This article defines an inverted Topp–Leone distribution. Several mathematical properties and maximum likelihood estimation of parameters of this distribution are considered. The shape of the distribution for different sets of parameters is discussed. Several mathematical properties such as the cumulative distribution function, mode, moment-generating function, survival function, hazard rate function, stress-strength reliability R, moments, Rényi entropy, Shannon entropy, Fisher information matrix, and partial ordering associated with this distribution, have been derived. Distributions of the sum and quotient of two independent inverted Topp–Leone variables have also been obtained. Full article

This paper introduces the Topp–Leone Heavy-Tailed Odd Burr X-G (TL-HT-OBX-G) family of distributions (FOD), designed to model diverse data patterns. The new distribution is an infinite linear combination of the established exponentiated-G distributions. We used the established properties of the exponentiated-G distribution to infer the properties of the new FOD. The properties considered include the quantile function, moments and moment generating functions, probability-weighted moments, order statistics, stochastic orderings, and Rényi entropy. Parameter estimation is performed using multiple techniques, such as maximum likelihood, least squares, weighted least squares, Anderson–Darling, Cramér–von Mises, and Right-Tail Anderson–Darling. The maximum likelihood estimation method produced superior results in the Monte Carlo simulation studies. A special case of the developed model was applied to three real-world datasets. The model parameters were estimated using the maximum likelihood method. The selected special model was compared to other competing models, and goodness-of-fit was evaluated by the use of several goodness-of-fit statistics. The developed model fit the selected real-world datasets better than all the selected competing models. The new FOD provides a new framework for data modeling in health sciences and reliability datasets. Full article

This paper presents a new model that surpasses traditional distributions, specifically the three-parameter distribution of the Inverse Power Entropy Chen (IPEC) model. In comparison to the existing distributions, the latest one presents an exceptionally diverse array of probability functions. The density and hazard rate functions have characteristics indicating that the model is adaptable to many types of data. The study explores the mathematical features of the IPEC distribution, including moments with some related measures, quantile function, Rényi entropy, Tsallis entropy, and order statistics. To estimate the parameters of the IPEC model, we utilized seven classical estimation strategies, including maximum likelihood estimators, Anderson–Darling estimators, right-tail Anderson–Darling estimators, Cramér–von Mises estimators, percentile estimators, least-squares estimators, and weighted least-squares estimators. To evaluate the efficacy of these estimating approaches across varying sample sizes, Monte Carlo simulations are performed. The efficacy of each estimator is evaluated through comparisons of average relative bias and mean squared error, highlighting their suitability for the used samples. Three applications utilize real-world datasets related to medical and physical fields, demonstrating the usefulness of the new model in relation to several established competitive models. This empirical investigation further supports the utility and adaptability of the inverse power entropy Chen model in capturing the intricacies of distinct datasets, hence delivering useful insights for practitioners in numerous domains. Full article

In this paper, the half-logistic generalized power Lindley distribution, a new two-parameter lifetime model for positive and heavy-tailed data, is proposed and studied. Several mathematical properties are derived, including closed-form expressions for the density, distribution, survival, hazard, and the Lambert W quantile function, as well as series expansions for moments, skewness, kurtosis, and Rényi entropy. Parameter estimation is performed using maximum likelihood and Bayesian methods, where Bayesian estimation is implemented via the Metropolis–Hastings algorithm. A Monte Carlo simulation study is conducted to evaluate the estimators’ performance, showing decreasing bias and mean squared error with larger samples. Finally, three real-world datasets are analyzed to demonstrate that the proposed distribution provides superior fit compared to Lindley-type competitors and the Weibull distribution, based on likelihood values, information criteria, and empirical diagnostics. Full article

This paper introduces the record-based transmuted Rayleigh distribution of order 3 (rbt-R), a three-parameter extension of the classical Rayleigh model designed to address data characterized by high skewness and heavy tails. While traditional generalizations of the Rayleigh distribution enhance model flexibility, they often lack sufficient adaptability to capture the complexity of empirical distributions encountered in applied statistics. The rbt-R model incorporates two additional shape parameters, a and b, enabling it to represent a wider range of distributional shapes. Parameter estimation for the rbt-R model is performed using the maximum likelihood method. Simulation studies are conducted to evaluate the asymptotic properties of the estimators, including bias and mean squared error. The performance of the rbt-R model is assessed through empirical applications to four datasets: nicotine yields and carbon monoxide emissions from cigarette data, as well as breaking stress measurements from carbon-fiber materials. Model fit is evaluated using standard goodness-of-fit criteria, including AIC, AIC_c, BIC, and the Kolmogorov–Smirnov statistic. In all cases, the rbt-R model demonstrates a superior fit compared to existing Rayleigh-based models, indicating its effectiveness in modeling highly skewed and heavy-tailed data. Full article

This research proposes a new method for time–frequency analysis, termed the Local Entropy Optimization–Adaptive Demodulation Reassignment Transform (LEOADRT), which is specifically designed to efficiently analyze complex, non-stationary mechanical vibration signals that exhibit multiple instantaneous frequencies or where the instantaneous frequency ridges are in close proximity to each other. The method introduces a demodulation term to account for the signal’s dynamic behavior over time, converting each component into a stationary signal. Based on the local optimal theory of Rényi entropy, the demodulation parameters are precisely determined to optimize the time–frequency analysis. Then, the energy redistribution of the ridges already generated in the time–frequency map is performed using the maximum local energy criterion, significantly improving time–frequency resolution. Experimental results demonstrate that the performance of the LEOADRT algorithm is superior to existing methods such as SBCT, EMCT, VSLCT, and GLCT, especially in processing complex non-stationary signals with non-proportionality and closely spaced frequency intervals. This method provides strong support for mechanical fault diagnosis, condition monitoring, and predictive maintenance, making it particularly suitable for real-time analysis of multi-component and cross-frequency signals. Full article

This study develops a new method for generating families of distributions based on the alpha power transformation and the trigonometric function, which enables enormous versatility in the resulting sub-models and enhances the ability to more accurately characterize tail shapes. This proposed family of distributions is characterized by a single parameter, which exhibits considerable flexibility in capturing asymmetric datasets, making it a valuable alternative to some families of distributions that require additional parameters to achieve similar levels of flexibility. The sine alpha power generated family is introduced using the proposed method, and some of its members and properties are discussed. A particular member, the sine alpha power-Weibull (SAP-W), is investigated in depth. Graphical representations of the new distribution display monotone and non-monotone forms, whereas the hazard rate function takes a reversed J shape, J shape, bathtub, increasing, and decreasing shapes. Various characteristics of SAP-W distribution are derived, including moments, rényi entropies, and order statistics. Parameters of SAP-W are estimated using the maximum likelihood technique, and the effectiveness of these estimators is examined via Monte Carlo simulations. The superiority and potentiality of the proposed approach are demonstrated by analyzing three real-life engineering applications. The SAP-W outperforms several competing models, showing its flexibility. Additionally, a novel-log location-scale regression model is presented using SAP-W. The regression model’s significance is illustrated through its application to real data. Full article

Given the increasing number of phenomena that demand interpretation and investigation, developing new distributions and families of distributions has become increasingly essential. This article introduces a novel family of distributions based on the exponentiated reciprocal of the hazard rate function named the new Lomax-G family of distributions. We demonstrate the family’s flexibility to predict a wide range of lifetime events by deriving its cumulative and probability density functions. The new Lomax–Weibull distribution (NLW) is studied as a sub-model, with analytical and graphical evidence indicating its efficiency for reliability analysis and complex data modeling. The NLW density encompasses a variety of shapes, such as symmetrical, semi-symmetrical, right-skewed, left-skewed, and inverted J shapes. Furthermore, its hazard function exhibits a broad range of asymmetric forms. Five estimation techniques for determining the parameters of the proposed NLW distribution include the maximum likelihood, percentile, least squares, weighted least squares, and Cramér–von Mises methods. The performance of the estimators of the studied inferential methods is investigated through a comparative Monte Carlo simulation study and numerical demonstration. Additionally, the effectiveness of the NLW is validated by means of four real-world datasets. The results indicate that the NLW distribution provides a more accurate fit than several competing models. Full article

In this article, we introduce a new three-parameter distribution called the discrete Weibull exponential (DWE) distribution, based on the use of a discretization technique for the Weibull-G family of distributions. This distribution is noteworthy, as its probability mass function presents both symmetric and asymmetric shapes. In addition, its related hazard function is tractable, exhibiting a wide range of shapes, including increasing, increasing–constant, uniform, monotonically increasing, and reversed J-shaped. We also discuss some of the properties of the proposed distribution, such as the moments, moment-generating function, dispersion index, Rényi entropy, and order statistics. The maximum likelihood method is employed to estimate the model’s unknown parameters, and these estimates are evaluated through simulation studies. Additionally, the effectiveness of the model is examined by applying it to three real data sets. The results demonstrate that, in comparison to the other considered distributions, the proposed distribution provides a better fit to the data. Full article

Limitations inherent to existing statistical distributions in capturing the complexities of real-world data often necessitate the development of novel models. This paper introduces the new exponential generalized inverse generalized Weibull (NEGIGW) distribution. The NEGIGW distribution boasts significant flexibility with symmetrical and asymmetrical shapes, allowing its hazard rate function to be adapted to many failure patterns observed in various fields such as medicine, biology, and engineering. Some statistical properties of the NEGIGW distribution, such as moments, quantile function, and Renyi entropy, are studied. Three methods are used for parameter estimation, including maximum likelihood, maximum product of spacing, and percentile methods. The performance of the estimation methods is evaluated via Monte Carlo simulations. The NEGIGW distribution excels in its ability to fit real-world data accurately. Five medical and engineering datasets are applied to demonstrate the superior fit of NEGIGW distribution compared to competing models. This compelling evidence suggests that the NEGIGW distribution is promising for lifetime data analysis and reliability assessments across different disciplines. Full article

Asymmetric distributions, as opposed to symmetric distributions, may be more resilient to extreme values or outliers. Furthermore, when data show substantial skewness, asymmetric distributions can shed light on the underlying processes or phenomena being investigated. In this direction, the size-biased Bilal distribution (SBBD) is suggested in this study as a generalization to the Bilal distribution. The length-biased and area-biased Bilal distributions are discussed in detail as two special cases. The main statistical properties of the distribution including the rth moment, coefficients of variation, skewness, kurtosis, moment generating function, incomplete moments, moments of residual life, harmonic mean, Fisher’s information, and the Rényi entropy as a measure of uncertainty are presented. Graphical representations of the cumulative distribution, probability density, odds, survival, hazard, reversed hazard rate, and cumulative hazard functions are presented for further explanation of the distribution behavior. In addition, the methods of moments and maximum likelihood estimates are taken into account for estimating the model parameters. A simulation study is carried out to see the efficiency of the maximum likelihood in terms of standard errors and bias. Real data sets of precipitation and myeloid leukemia patients are considered to show the practical significance of the suggested distributions as an alternative to some well-known distributions such as the Rama, Rani, Bilal, and exponential distributions. It is found that the size-biased Bilal distribution is right-skewed and has a superior fitting performance compared to the other distributions in this study. Full article

In this study, we introduce a new generalized family of distributions called the Exponentiated Half Logistic-Harris-G (EHL-Harris-G) distribution, which extends the Harris-G distribution. The motivation for introducing this generalized family of distributions lies in its ability to overcome the limitations of previous families, enhance flexibility, improve tail behavior, provide better statistical properties and find applications in several fields. Several statistical properties, including hazard rate function, quantile function, moments, moments of residual life, distribution of the order statistics and Rényi entropy are discussed. Risk measures, such as value at risk, tail value at risk, tail variance and tail variance premium, are also derived and studied. To estimate the parameters of the EHL-Harris-G family of distributions, the following six different estimation approaches are used: maximum likelihood (MLE), least-squares (LS), weighted least-squares (WLS), maximum product spacing (MPS), Cramér–von Mises (CVM), and Anderson–Darling (AD). The Monte Carlo simulation results for EHL-Harris-Weibull (EHL-Harris-W) show that the MLE method allows us to obtain better estimates, followed by WLS and then AD. Finally, we show that the EHL-Harris-W distribution is superior to some other equi-parameter non-nested models in the literature, by fitting it to two real-life data sets from different disciplines. Full article

This article utilizes improved adaptive progressively Type-II censored data to estimate the entropy of the inverse Weibull distribution. Rényi, q, and Shannon entropy measurements are used to define entropy to achieve this objective. Both point and interval estimations of the entropy quantities are investigated through the maximum likelihood and maximum product of spacing methods. Two parametric bootstrap confidence intervals based on the two estimation techniques are also considered for the various entropy measures. A Monte Carlo simulation study is conducted to investigate how estimates behave at various sample sizes and different censoring schemes based on some statistical measurements. The simulations demonstrate that, as anticipated, when the sample size grows, the estimation accuracy also grows. Furthermore, they show that the estimated entropy measures get closer to the actual entropy values when the censoring level decreases. For purposes of explanation, two applications to actual datasets are taken into consideration. The results verified that the adaptive or improved adaptive progressive censoring schemes give more information about data than the conventional progressive censoring scheme in terms of minimum entropy measures. Full article

In this article, we introduce the Kavya–Manoharan generalized inverse Kumaraswamy (KM-GIKw) distribution, which can be presented as an improved version of the generalized inverse Kumaraswamy distribution with three parameters. It contains numerous referenced lifetime distributions of the literature and a large panel of new ones. Among the essential features and attributes covered in our research are quantiles, moments, and information measures. In particular, various entropy measures (Rényi, Tsallis, etc.) are derived and discussed numerically. The adaptability of the KM-GIKw distribution in terms of the shapes of the probability density and hazard rate functions demonstrates how well it is able to fit different types of data. Based on it, an acceptance sampling plan is created when the life test is truncated at a predefined time. More precisely, the truncation time is intended to represent the median of the KM-GIKw distribution with preset factors. In a separate part, the focus is put on the inference of the KM-GIKw distribution. The related parameters are estimated using the Bayesian, maximum likelihood, and maximum product of spacings methods. For the Bayesian method, both symmetric and asymmetric loss functions are employed. To examine the behaviors of various estimates based on criterion measurements, a Monte Carlo simulation research is carried out. Finally, with the aim of demonstrating the applicability of our findings, three real datasets are used. The results show that the KM-GIKw distribution offers superior fits when compared to other well-known distributions. Full article

In this article, we intend to introduce and study a new two-parameter distribution as a new extension of the power Topp–Leone (PTL) distribution called the Kavya–Manoharan PTL (KMPTL) distribution. Several mathematical and statistical features of the KMPTL distribution, such as the quantile function, moments, generating function, and incomplete moments, are calculated. Some measures of entropy are investigated. The cumulative residual Rényi entropy (CRRE) is calculated. To estimate the parameters of the KMPTL distribution, both maximum likelihood and Bayesian estimation methods are used under simple random sample (SRS) and ranked set sampling (RSS). The simulation study was performed to be able to verify the model parameters of the KMPTL distribution using SRS and RSS to demonstrate that RSS is more efficient than SRS. We demonstrated that the KMPTL distribution has more flexibility than the PTL distribution and the other nine competitive statistical distributions: PTL, unit-Gompertz, unit-Lindley, Topp–Leone, unit generalized log Burr XII, unit exponential Pareto, Kumaraswamy, beta, Marshall-Olkin Kumaraswamy distributions employing two real-world datasets. Full article