In this paper, we present a new family of continuous distributions known as the type I half logistic Burr X-G. The proposed family’s essential mathematical properties, such as quantile function (QuFu), moments (Mo), incomplete moments (InMo), mean deviation (MeD), Lorenz (Lo) and Bonferroni (Bo) curves, and entropy (En), are provided. Special models of the family are presented, including type I half logistic Burr X-Lomax, type I half logistic Burr X-Rayleigh, and type I half logistic Burr X-exponential. The maximum likelihood (MLL) and Bayesian techniques are utilized to produce parameter estimators for the recommended family using type II censored data. Monte Carlo simulation is used to evaluate the accuracy of estimates for one of the family’s special models. The COVID-19 real datasets from Italy, Canada, and Belgium are analysed to demonstrate the significance and flexibility of some new distributions from the family.

The aim of this paper is devoted to the problem of comparative life tests under joint censoring samples from an exponential distribution with competing risks model. This problem is considered under the consideration that only two causes of failure are occurring and the units come from two production lines such that the exponential failure time of units is censored under a hybrid progressive Type-I censoring scheme. Maximum likelihood estimation and different Bayes methods of estimation are discussed. The asymptotic confidence intervals as well as the Bayes credible intervals are established. A real data set representing time to failure on two groups of strain male mice receiving radiation is analyzed for illustrative purposes. All theoretical results are assessed and compared through the Monte Carlo study.

In this paper a new inverse Kumaraswamy distribution has been proposed. The recurrence relation for moments of dual generalized order statistics has been presented for the new inverse Kumaraswamy distribution. These include the recurrence relations for single, inverse, product and ratio moments of dual generalized order statistics for the new inverse Kumaraswamy distribution. Special cases of the recurrence relations have also been obtained.

The main purpose of this note is to provide further properties of discrete lifetime distributions based on variance residual lifetimes (VRL). New discrete aging classes are introduced in terms of discrete version of VRL. We demonstrate closure of discrete variance residual lifetime under convolution and mixing.

The Kumaraswamy distribution is an important probability distribution used to model several hydrological problems as well as various natural phenomena whose process values are bounded on both sides. In this paper, we introduce a new family of inverse Kumaraswamy distribution and then explore its statistical properties. Conventional maximum likelihood estimators are considered for the parameters of this distribution and estimation based on dual generalized order statistics is outlined. A particular sub-model of this family; namely, the inverse Kumaraswamy- Weibull distribution is considered and some of its statistical properties are obtained. Estimation efficiency is numerically evaluated via a simulation study and two real-data applications of the proposed distribution are provided as well.