Weibull-Linear Exponential Distribution and Its Applications

In this article, a new four-parameter lifetime distribution, namely, the Weibull-Linear exponential distribution is defined and studied. Several of its structural properties such as quartiles, moments, mean waiting time, mean residual lifetime, Renyi entropy, mode, and order statistics are derived. Based on the idea of the Weibull T − X family, the new density function of this model is developed. The model parameters, as well as some of the lifetime parameters (reliability and failure rate functions), are estimated using the maximum likelihood method. Asymptotic confidence intervals estimates of the model parameters are also evaluated by using the Fisher information matrix. Moreover, to construct the asymptotic confidence intervals of the reliability and failure rate functions, we need to find their variance of them, which are approximated by the delta method. A real data set is used to illustrate the application of the Weibull-Linear Exponential distribution

Classical and Bayesian estimation for the truncated inverse power Ailamujia distribution with applications

In this study, we suggest the truncated version of the inverse power Ailamujia distribution, which is more flexible than other well-known distributions. Statistical properties of the new distribution are considered, such as moments, moment generating function, incomplete moments, quantile function, order statistics, and entropy. We discuss various methods of estimation, such as the method of maximum likelihood, methods of least squares and weighted least squares, the method of the maximum product of spacings, the method of Cramer and Von-Mises, methods of Anderson and Darling and right-tail Anderson and Darling, the method of percentiles, and the Bayesian method. Simulation is implemented to study the performance of estimates. We introduce two real data applications, showing that the new distribution can provide better fits than some other corresponding distributions

A Unit Half-Logistic Geometric Distribution and Its Application in Insurance

A new one parameter distribution recently was proposed for modelling lifetime data called half logistic-geometric (HLG) distribution. In this paper, appropriate transformation is considered for HLG distribution and a new distribution is derived called unit half logistic-geometric (UHLG) distribution for modelling bounded data in the interval (0, 1). Some important statistical properties are investigated with a closed form quantile function. Some methods of parameter estimation are introduced to evaluate the distribution parameter and a simulation study is introduced to compare these different methods. A real data application in the insurance field is introduced to show the flexibility of the new distribution modelling such data comparing with other distributions

The Odd Generalized Exponential Linear Failure Rate Distribution

In this paper we study the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median and the mode are investigated. The method of maximum likelihood is used for estimating the model parameters. An applications to real data is carried out to illustrate that the new distribution is more flexible and effective than other popular distributions in modeling lifetime data