We prepare a new method to generate family of distributions. Then, a family of univariate distributions generated by the Gamma random variable is defined. The generalized gamma-Weibull (GGW) distribution is studied as a special case of this family. Certain mathematical properties of moments are provided. To estimate the model parameters, the maximum likelihood estimators and the asymptotic distribution of the estimators are discussed. Certain characterizations of GGW distribution are presented. Finally, the usefulness of the new distribution, as well as its effectiveness in comparison with other distributions, are shown via an application of a real data set.
In this paper, we introduce a new class of beta-complementary exponential power series distributions, which is obtained by replacing the cumulative distribution function of the complementary exponential power series distributions in the logit of a beta random variable. This new class of distributions contains some new submodels, such as beta-complementary exponential geometric, beta-complementary exponential Poisson, beta-complementary exponential binomial, beta-complementary exponential logarithmic, and complementary exponential power series distributions. A general class of distributions is presented and some various properties are obtained in this paper. We characterize the beta-complementary exponential geometric distribution as one of the most applicable distributions in this class. Some mathematical properties of the beta-complementary exponential geometric distribution are reached in terms of the corresponding properties of the complementary exponential geometric and beta exponential distributions. We present expressions for the probability density function, cumulative distribution function, moment generating function, and moments. The estimation of parameters is approached by the maximum likelihood estimation procedure, and the expected information matrix is derived. The flexibility of the distribution is illustrated in application of a real data set.
This paper introduces a special case of weighted-k-out-of-n:G system formed from two types of nonidentical components with different weights. This system consists of n nonidentical components each with its own positive integer-valued weight which are categorized into two groups with respect to their duties and services. In fact, we have a system consisting n components such that n1 of them each with its own weight 𝜔 i and reliability p1i and n2 of them each with its own weight 𝜔 * i and reliability p2i. If the total weights of the functioning components exceeds a prespecified threshold k, the system is supposed to work. The reliability of system is obtained based on the total weight of all working components in both group. The survival function and mean time to failure are presented. Also, the component importance of this system are studied.
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