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This article suggests a new method to expand a family of life distributions by adding a parameter to the family, increasing its flexibility. It is called the extended Modi-G family of distributions. We derived the general statistical properties of the proposed family. Different methods of estimation were presented to estimate the parameters for the proposed family, such as maximum likelihood, ordinary least square, weighted least square, Anderson Darling, right-tailed Anderson-Darling, Cramér-von Mises, and maximum product of spacing methods. A special sub-model with three parameters called extended Modi exponential distribution was derived along with different shapes of its density and hazard functions. Randomly generated data sets and different estimation methods were used to illustrate the behavior of parameters of the proposal sub-model. To illustrate the importance of the proposed family over the other well-known methods, applications to medicine and geology data sets were analyzed. [ABSTRACT FROM AUTHOR]

This paper discussed gull alpha power Weibull distribution with a three-parameter. Different statistical inference methods of Gull Alpha Power Weibull distribution parameters have been obtained, estimated, and evaluated. Then, the results are compared to find a suitable model. The unknown parameters of the published Gull Alpha Power Weibull distribution are analyzed. Seven estimation methods are maximum likelihood, Anderson–Darling, right-tail Anderson–Darling, Cramér–von Mises, ordinary least-squares, weighted least-squares, and maximum product of spacing. In addition, the performance of this distribution is computed using the Monte Carlo method, and the limited sample features of parameter estimates for the proposed distribution are analyzed. In light of the importance of heavy-tailed distributions, actuarial approaches are employed. Applying actuarial criteria such as value at risk and tail value at risk to the suggested distribution shows that the model under study has a larger tail than the Weibull distribution. Two real-world COVID-19 infection datasets are used to evaluate the distribution. We analyze the existence and uniqueness of the log-probability roots to establish that they represent the global maximum. We conclude by summarizing the outcomes reported in this study. [ABSTRACT FROM AUTHOR]

This paper introduced and investigated the power unit inverse Lindley distribution (PUILD), a novel two-parameter generalization of the famous unit inverse Lindley distribution. Among its notable functional properties, the corresponding probability density function can be unimodal, decreasing, increasing, or right-skewed. In addition, the hazard rate function can be increasing, U-shaped, or N-shaped. The PUILD thus takes advantage of these characteristics to gain flexibility in the analysis of unit data compared to the former unit inverse Lindley distribution, among others. From a theoretical point of view, many key measures were determined under closed-form expressions, including mode, quantiles, median, Bowley's skewness, Moor's kurtosis, coefficient of variation, index of dispersion, moments of various types, and Lorenz and Bonferroni curves. Some important measures of uncertainty were also calculated, mainly through the incomplete gamma function. In the statistical part, the estimation of the parameters involved was studied using fifteen different methods, including the maximum likelihood method. The invariant property of this approach was then used to efficiently estimate different uncertainty measures. Some simulation results were presented to support this claim. The significance of the PUILD underlying model compared to several current statistical models, including the unit inverse Lindley, exponentiated Topp-Leone, Kumaraswamy, and beta and transformed gamma models, was illustrated by two applications using real datasets. [ABSTRACT FROM AUTHOR]

The arctan uniform distribution (AUD) is a brand-new bounded distribution that may be used for modeling a variety of existing bounded real-world datasets. Ranked set sampling (RSS) is a useful technique for parameter estimation when accurate measurement of the observation is challenging and/or expensive. In the current study, the parameter estimator of the AUD is addressed based on RSS and simple random sampling (SRS) techniques. Some of the popular conventional estimating techniques are considered. The efficiency of the produced estimates is compared using a Monte Carlo simulation. It appears that the maximum product spacing method has an advantage in assessing the quality of proposed estimates based on the outcomes of our simulations for both the SRS and RSS datasets. In comparison to estimates produced from the SRS datasets, it can be seen that those from the RSS datasets are more reliable. This implies that RSS is a more effective sampling technique in terms of generating estimates with a smaller mean squared error. The benefit of the RSS design over the SRS design is further supported by real data results. [ABSTRACT FROM AUTHOR]

In this article, a new three-parameter lifetime model called the Gull alpha power exponentiated exponential (GAPEE) distribution is introduced and studied by combining the Gull alpha power family of distributions and the exponentiated exponential distribution. The shapes of the probability density function (PDF) for the GAPEE distribution can be asymmetric shapes, like unimodal, decreasing, and right-skewed. In addition, the shapes of the hazard rate function (hrf) for the GAPEE distribution can be increasing, decreasing, and upside-down shaped. Several statistical features of the GAPEE distribution are computed. Eight estimation methods such as the maximum likelihood, Anderson-Darling, right-tail Anderson-Darling, left-tailed Anderson-Darling, Cramer-von Mises, least-squares, weighted least-squares, and maximum product of spacing are discussed to estimate the parameters of the GAPEE distribution. The flexibility and the importance of the GAPEE distribution were demonstrated utilizing three real-world datasets related to medical sciences. The GAPEE distribution is extremely adaptable and outperforms several well-known statistical models. A bivariate step-stress accelerated life test based on progressive type-I censoring using the model is presented. Minimizing the asymptotic variance of the maximum likelihood estimate of the log of the scale parameter at design stress under progressive type-I censoring yields an expression for the ideal test plan under progressive type-I censoring. [ABSTRACT FROM AUTHOR]

This article introduces a new statistical distribution called the power unit Burr-XII distribution, which is an extension of the Burr XII distribution obtained through a power transform. This paper investigates several statistical properties of this new model, including mode, moments, moment generating and characteristic functions, entropy, and Bonferroni and Lorenz curves. In addition, various classical estimators for the parameters of the power unit Burr-XII distribution are evaluated, including maximum likelihood estimates, ordinary least squares estimates, maximum product of interval estimates, Anderson–Darling, right and left tail Anderson–Darling, and Cramer–von Mises estimators. This study provides tables and graphs to illustrate the performance of these methods under different scenarios and sample sizes. The results of the proposed distribution in different fields of application are shown using the mortality rates of COVID-19 patients in Spain and flood data from 20 observations. As a result of both applications, it was observed that the proposed distribution gave better results compared to other well-known distributions, such as the beta distribution, transformed gamma distribution, log-weighted power distribution, transmuted power distribution, Kumaraswamy distribution, Topp–Leone distribution, exponentiated reduce Kies distribution, and exponentiated Topp–Leone distribution. [ABSTRACT FROM AUTHOR]

In this paper, a new flexible two-parameter family of distributions is introduced. Some mathematical properties, such as asymptotic behavior, moments, stochastic order, entropy, and quantile function, are examined. A special case of this family is introduced called Gemeay–Zeghdoudi distribution. The unknown parameters of the Gemeay–Zeghdoudi distribution are estimated via many estimators. The efficiency of the estimators is compared with a Monte Carlo simulation. The applicability of the new distribution is illustrated by the annual maximum flood and survival times of patients with breast cancer real data analyses. [ABSTRACT FROM AUTHOR]