Journal of Data Science

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: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.

The concept of ranked set sampling (RSS) is applicable whenever ranking on a set of sampling units can be done easily by a judgment method or based on an auxiliary variable. In this work, we consider a study variable 𝑌 correlated with auxiliary variable 𝑋 which is used to rank the sampling units. Further (𝑋, 𝑌) is assumed to have Morgenstern type bivariate generalized uniform distribution. We obtain an unbiased estimator of a scale parameter associated with the study variable 𝑌 based on different RSS schemes and censored RSS. Efficiency comparison study of these estimators is also performed and presented numerically.

Abstract: In this paper, we obtain several estimators of a scale parameter of Morgenstern type bivariate uniform distribution (MTBUD) based on the observations made on the units of the ranked set sampling regarding the study variable Y which is correlated with the auxiliary variable X, when (X, Y ) follows a MTBUD. Efficiency comparisons among these estimators are also made in this work. Finally, we illustrate the methods developed by using a real data set.