A new extended gumbel distribution: Properties and application

Tests of fit for the power function lognormal distribution

In this study, tests of fit for the power function lognormal distribution is considered. The probability plot, probability plot correlation coefficient, and goodness-of-fit tests-the Kolmogorov-Smirnov (KS), Cramér-von Mises (CvM), and Anderson-Darling (AD) tests are provided. Tables of critical values are presented by using simulation techniques, and the AD test outperforms KS and CvM tests based on power comparisons. Finally, to illustrate these test procedures, we fit this distribution to the data which represent the survival times of 121 breast cancer patients from one hospital.

Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications

In this study, we propose a generalized Marshall-Olkin exponentiated exponential distribution as a submodel of the family of generalized Marshall-Olkin distribution. Some statistical properties of the proposed distribution are examined such as moments, the moment-generating function, incomplete moment, and Lorenz and Bonferroni curves. We give five estimators for the unknown parameters of the proposed distribution based on maximum likelihood, least squares, weighted least squares, and the Anderson-Darling and Cramer-von Mises methods of estimation. To investigate the finite sample properties of the estimators, a comprehensive Monte Carlo simulation study is conducted for the models with three sets of randomly selected parameter values. Finally, four different real data applications are presented to demonstrate the usefulness of the proposed distribution in real life.

A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data

With the aim of identifying a probability model that not only correctly describes the stochastic behavior of extreme environmental factors such as excess rain, acid rain pH level, and concentrations of ozone, but also measures concentrations of NO2 and leads deliberations, etc., for a specific site or multiple site forms as well as for life testing experiments, we introduced a novel class of distributions known as the Sine Burr X−G family. Some exceptional prototypes of this class are proposed. Statistical assets of the presented class, such as density function, complete and incomplete moments, average deviation, and Lorenz and Bonferroni graphs, are proposed. Parameter estimation is made via the likelihood method. Moreover, the application is explained by using four real data sets. We have also illustrated the significance and elasticity of the proposed class in the above-mentioned stochastic phenomenon.