We introduce a new class of continuous distributions called the Topp Leone odd Lindley-G family. Some mathematical properties of the new family such as; the raw and incomplete moments, moment generating function, stress strength model, Rényi entropy, probability weighted moments and order statistics are investigated. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. The potentiality of the new family is illustrated by means of three applications to real data sets.

In this paper, we propose a new class of continuous distributions called the exponentiated generalized Topp Leone-G family that extends the Topp Leone-G family introduced by Al-Shomrani et al. (2016). We derive explicit expressions for certain mathematical properties of the new family such as; ordinary and incomplete moments, generating functions, reliability analysis, Lorenz and Bonferroni curves, Rényi entropy, stress strength model, moment of residual and reversed residual life, order statistics and extreme values. We discuss the maximum likelihood estimates and the observed information matrix for the model parameters. Two real data sets are used to illustrate the flexibility of the new family.

In this paper we introduce a new generalization of the Burr-XII distribution using the genesis of the Topp-Leone distribution and is named as Topp-Leone Burr-XII (TLBXII) distribution. The statistical properties of this distribution including the mean, variance, coefficient of variation, quantile function, median, ordinary and incomplete moments, skewness, kurtosis, moment and probability generating functions, reliability analysis, Lorenz, Bonferroni and Zenga curves, Rényi of entropy and order statistics are studied. We consider the method of maximum likelihood for estimating the model parameters and the observed information matrix is derived. Three real data sets are presented to demonstrate the effectiveness of the new model.

A new four-parameter lifetime distribution (called the Topp Leone Weibull-Lomax distribution) is proposed in this paper. Different mathematical properties of the proposed distribution were studied which include quantile function, ordinary and incomplete moments, probability weighted moment, conditional moments, order statistics, stochastic ordering, and stress-strength reliability parameter. The regression model and the residual analysis for the proposed model were also carried out. The model parameters were estimated by using the maximum likelihood criterion and the behaviour of these estimated parameters were examined by conducting a simulation study. The importance and flexibility of the proposed distribution have been proved empirically by using four separate data sets.

This paper introduces the Bayesian and E-Bayesian estimation for the shape parameter of the Kumaraswamy distribution based on type-II censored schemes. These estimators are derived under symmetric loss function [squared error loss (SELF))] and three asymmetric loss functions [LINEX loss function (LLF), Degroot loss function (DLF) and Quadratic loss function (QLF)]. Monte Carlo simulation is performed to compare the E-Bayesian estimators with the associated Bayesian estimators in terms of Mean Square Error (MSE).