Journal of Data Science

Abstract: Ranked set sampling and some of its variants have been applied successfully in different areas of applications such as industrial statistics, economics, environmental and ecological studies, biostatistics, and statistical genetics. Ranked set sampling is a sampling method that more efficient than simple random sampling. Also, it is well known that Fisher information of a ranked set sample (RSS) is larger than Fisher information of a simple random sample (SRS) of the same size about the unknown parameter of the underlying distribution in parametric inference. In this paper, we consider the Farlie-Gumbel-Morgenstern (FGM) family and study the information measures such as Shannon’s entropy, Rényi entropy, mutual information, and Kullback-Leibler (KL) information of RSS data. Also, we investigate their properties and compare them with a SRS data.

This paper introduces a new three-parameter distribution called inverse generalized power Weibull distribution. This distribution can be regarded as a reciprocal of the generalized power Weibull distribution. The new distribution is characterized by being a general formula for some well-known distributions, namely inverse Weibull, inverse exponential, inverse Rayleigh and inverse Nadarajah-Haghighi distributions. Some of the mathematical properties of the new distribution including the quantile, density, cumulative distribution functions, moments, moments generating function and order statistics are derived. The model parameters are estimated using the maximum likelihood method. The Monte Carlo simulation study is used to assess the performance of the maximum likelihood estimators in terms of mean squared errors. Two real datasets are used to demonstrate the flexibility of the new distribution as well as to demonstrate its applicability.

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.

Abstract:A new generalized two-parameter Lindley distribution which offers more flexibility in modeling lifetime data is proposed and some of its mathematical properties such as the density function, cumulative distribution function, survival function, hazard rate function, mean residual life function, moment generating function, quantile function, moments, Renyi entropy and stochastic ordering are obtained. The maximum likelihood estimation method was used in estimating the parameters of the proposed distribution and a simulation study was carried out to examine the performance and accuracy of the maximum likelihood estimators of the parameters. Finally, an application of the proposed distribution to a real lifetime data set is presented and its fit was compared with the fit attained by some existing lifetime distributions.

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.