Distributional Properties of Record Values of the Ratio of Independent Exponential and Gamma Random Variables

Both exponential and gamma distributions play pivotal roles in the study of records because of their wide applicability in the modeling and analysis of life time data in various fields of applied sciences. In this paper, a distribution of record values of the ratio of independent exponential and gamma random variables is presented. The expressions for the cumulative distribution functions, moments, hazard function and Shannon entropy have been derived. The maximum likelihood, method of moments and minimum variance linear unbiased estimators of the parameters, using record values and the expressions to calculate the best linear unbiased predictor of record values, are obtained.