A New Inverse Rayleigh Distribution with Applications of COVID-19 Data: Properties, Estimation Methods and Censored Sample

This paper aims at modelling the COVID-19 spread in the United Kingdom and the United States of America, by specifying an optimal statistical univariate model. A new lifetime distribution with three-parameters is introduced by a combination of inverse Rayleigh distribution and odd Weibull family of distributions to formulate the odd Weibull inverse Rayleigh (OWIR) distribution. Some of the mathematical properties of the OWIR distribution are discussed as linear representation, quantile, moments, function of moment production, hazard rate, stress-strength reliability, and order statistics. Maximum likelihood, maximum product spacing, and Bayesian estimation method are applied to estimate the unknown parameters of OWIR distribution. The parameters of the OWIR distribution are estimated under the progressive type-II censoring scheme with random removal. A numerical result of a Monte Carlo simulation is obtained to assess the use of estimation methods

A New Inverse Rayleigh Distribution with Applications of COVID-19 Data: Properties, Estimation Methods and Censored Sample

This paper aims at modelling the COVID-19 spread in the United Kingdom and the United States of America, by specifying an optimal statistical univariate model. A new lifetime distribution with three-parameters is introduced by a combination of inverse Rayleigh distribution and odd Weibull family of distributions to formulate the odd Weibull inverse Rayleigh (OWIR) distribution. Some of the mathematical properties of the OWIR distribution are discussed as linear representation, quantile, moments, function of moment production, hazard rate, stress-strength reliability, and order statistics. Maximum likelihood, maximum product spacing, and Bayesian estimation method are applied to estimate the unknown parameters of OWIR distribution. The parameters of the OWIR distribution are estimated under the progressive type-II censoring scheme with random removal. A numerical result of a Monte Carlo simulation is obtained to assess the use of estimation methods

Characterizations and Infinite Divisibility of Certain Recently Introduced Distributions IV

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work contains a good number of reintroduced distributions and may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future

Reliability analysis of s-out-of-k multicomponent stress-strength system with dependent strength elements based on copula function

This paper considers the reliability analysis of a multicomponent stress-strength system which has $k$ statistically independent and identically distributed strength components, and each component is constructed by a pair of statistically dependent elements. These elements are exposed to a common random stress, and the dependence among lifetimes of elements is generated by Clayton copula with unknown copula parameter. The system is regarded to be operating only if at least $s$($1 \leq s \leq k$) strength variables in the system exceed the random stress. The maximum likelihood estimates (MLE) of unknown parameters and system reliability is established and associated asymptotic confidence interval is constructed using the asymptotic normality property and delta method, and the bootstrap confidence intervals are obtained using the sampling theory. Finally, Monte Carlo simulation is conducted to support the proposed model and methods, and one real data set is analyzed to demonstrate the applicability of our study