In this study, we introduce a new family of continuous distributions with one extra shape parameter, called the Burr-Hatke-G family, based on the Burr-Hatke differential equation. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. Moreover, the log-Burr-Hatke-Weibull regression model based on new the generated family is introduced. The usefulness of the proposed family is demonstrated by means of the three real data applications. Empirical results indicate that the proposed family provides more realistic fits than other well-known family of distributions.

In this paper, we first study a new two parameter lifetime distribution. This distribution includes “monotone” and “non-monotone” hazard rate functions which are useful in lifetime data analysis and reliability. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, δ-entropy, order statistics and probability weighted moments are derived. Non-Bayesian estimation methods such as the maximum likelihood, Cramer-Von-Mises, percentile estimation, and L-moments are used for estimating the model parameters. The importance and flexibility of the new distribution are illustrated by means of two applications to real data sets. Using the approach of the Bagdonavicius–Nikulin goodness-of-fit test for the right censored validation, we then propose and apply a modified chi-square goodness-of-fit test for the Burr X Weibull model. The modified goodness-of-fit statistics test is applied for the right censored real data set. Based on the censored maximum likelihood estimators on initial data, the modified goodness-of-fit test recovers the loss in information while the grouped data follows the chi-square distribution. The elements of the modified criteria tests are derived. A real data application is for validation under the uncensored scheme.

In this paper, a new class of continuous distributions with two extra positive parameters is introduced and is called the Type II General Exponential (TIIGE) distribution. Some special models are presented. Asymptotics, explicit expressions for the ordinary and incomplete moments, moment residual life, reversed residual life, quantile and generating functions and stress-strengh reliability function are derived. Characterizations of this family are obtained based on truncated moments, hazard function, conditional expectation of certain functions of the random variable are obtained. The performance of the maximum likelihood estimators in terms of biases, mean squared errors and confidence interval length is examined by means of a simulation study. Two real data sets are used to illustrate the application of the proposed class.

In this paper, a multicomponent system which has k independent and identical strength components $X_1,X_2,\dots ,X_k$ is considered. Each component is exposed to a common random stress Y when distributions are generalized logistic. This system is operating or failing only if at least s out of k ( $1\le s\le k$) strength variables exceeds the random stress. The Bayesian and classical inferences of multicomponent stress-strength reliability under the generalized logistic distribution are studied. The small sample comparison of the reliability estimates is made through Monte Carlo simulation and asymptotic confidence interval is obtained based on maximum likelihood estimation. Also the highest posterior density credible interval is calculated based on Bayesian estimation with Gibbs and Metropolis Hastings algorithms. Finally analysis of a real data set has been presented for illustrative purposes too.

We introduce a new family of continuous distributions and study the mathematical properties of the new family. Some useful characterizations based on the ratio of two truncated moments and hazard function are also presented. We estimate the model parameters by the maximum likelihood method and assess its performance based on biases and mean squared errors in a simulation study framework.