Journal of Data Science

In this paper, we introduce a new family of univariate distributions with two extra positive parameters generated from inverse Weibull random variable called the inverse Weibull generated (IW-G) family. The new family provides a lot of new models as well as contains two new families as special cases. We explore four special models for the new family. Some mathematical properties of the new family including quantile function, ordinary and incomplete moments, probability weighted moments, Rѐnyi entropy and order statistics are derived. The estimation of the model parameters is performed via maximum likelihood method. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.

Abstract: Suppose that an order restriction is imposed among several means in time series. We are interested in testing the homogeneity of these unknown means under this restriction. In the present paper, a test based on the isotonic regression is done for monotonic ordered means in time series with stationary process and short range dependent sequences errors. A test statistic is proposed using the penalized likelihood ratio (PLR) approach. Since the asymptotic null distribution of test statistic is complicated, its critical values are computed by using Monte Carlo simulation method for some values of sample sizes at different significance levels. The power study of our test statistic is provided which is more powerful than that of the test proposed by Brillinger (1989). Finally, to show the application of the proposed test, it is applied to real dataset contains monthly Iran rainfall records.

A new four parameter extreme value distribution is defined and studied. Various structural properties of the proposed distribution including ordinary and incomplete moments, generating functions, residual and reversed residual life functions, order statistics are investigated. Some useful characterizations based on two truncated moments as well as based on the reverse hazard function and on certain functions of the random variable are presented. The maximum likelihood method is used to estimate the model parameters. Further, we propose a new extended regression model based on the logarithm of the new distribution. The new distribution is applied to model three real data sets to prove empirically its flexibility.

The Topp-Leone distribution is an attractive model for life testing and reliability studies as it acquires a bathtub shaped hazard function. In this paper, we introduce a new family of distributions, depending on Topp–Leone random variable as a generator, called the Type II generalized Topp– Leone–G (TIIGTL-G) family. Its density function can be unimodel, leftskewed, right-skewed, and reversed-J shaped, and has increasing, decreasing, upside-down, J and reversed-J hazard rates. Some special models are presented. Some of its statistical properties are studied. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Rényi entropy and order statistics are derived. The method of maximum likelihood is used to estimate the model parameters. The importance of one special model; namely; the Type II generalized Topp–Leone exponential is illustrated through two real data sets.

Abstract: In this small note we have established some new explicit expressions for ratio and inverse moments of lower generalized order statistics for the Marshall-Olkin extended Burr type XII distribution. These explicit expressions can be used to develop the relationship for moments of ordinary order statistics, record statistics and other ordered random variable techniques. Further, a characterization result of this distribution has been considered on using the conditional moment of the lower generalized order statistics.