Exponential-modified discrete Lindley distribution

Abstract

In this study, we have considered a series system composed of stochastically independent M-component where M is a random variable having the zero truncated modified discrete Lindley distribution. This distribution is newly introduced by transforming on original parameter. The properties of the distribution of the lifetime of above system have been examined under the given circumstances and also parameters of this new lifetime distribution are estimated by using moments, maximum likelihood and EM-algorithm.

Exponential-Discrete Lindley Distribution: Properties and Applications

“…[1] suggested to use Exponential-Geometric (E-G) and [2] suggested to use Exponential-Poisson (E-P) distributions. On the other hand, [11] and [8] have proposed two-component mixed exponential distribution (2MED) and exponential modified discrete Lindley distribution (EMDL) for modeling this data set. According to reported result of [12], Exponentiated exponential (EE) distribution is also used for modeling this data set.…”

“…[7] have considered the Lindley distribution which is composed of the mixture of the exponential and the gamma distributions. Moreover, [8] proposed a new lifetime distribution by compounding exponential and modified-zero-truncated discrete Lindley distributions.…”

Univariate and multivariate mixtures of exponential distributions, with applications in risk modeling

“…Mixed exponential distributions are also frequently used as life‐time distributions in the context of failure data analysis. Several mixed exponential distributions have been proposed in the literature in such a context, see, for example, References 9‐16, and 17. Mixed exponential distributions have a decreasing failure rate (DFR) making them very useful in reliability theory (see, e.g., Reference 18 for a proof of the DFR property of mixtures of distributions with a constant hazard rate).…”