Concept

Exponential-logarithmic distribution

Summary
In probability theory and statistics, the Exponential-Logarithmic (EL) distribution is a family of lifetime distributions with decreasing failure rate, defined on the interval [0, ∞). This distribution is parameterized by two parameters p\in(0,1) and \beta >0. Introduction The study of lengths of the lives of organisms, devices, materials, etc., is of major importance in the biological and engineering sciences. In general, the lifetime of a device is expected to exhibit decreasing failure rate (DFR) when its behavior over time is characterized by 'work-hardening' (in engineering terms) or 'immunity' (in biological terms). The exponential-logarithmic model, together with its various properties, are studied by Tahmasbi and Rezaei (2008). This model is obtained under the concept of population heterogeneity (through the process of compounding). Properties of the distribution Distribution The probability density fu
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