Pak.j.stat.oper.res. Vol.19 No. 2 2023 pp 241-256 DOI: http://dx.doi.org/10.18187/pjsor.v19i2.3255 GOLD DISTRIBUTION: Another Look on the Generalization of Lindely Distribution 241 GOLD DISTRIBUTION Another Look on the Generalization of Lindely Distribution Mohammad Al-Talib 1* , Amjad Al-Nasser 2 , Enrico Ciavolino 3 * Corresponding Author 1. Department of Statistics, Yarmouk University, 21163 Irbid, Jordan, m.altalib@yu.edu.jo 2. Department of Statistics, Yarmouk University, 21163 Irbid, Jordan, amjadn@yu.edu.jo 3. Dipartimento di Filosofia e Scienze Sociali, Università del Salento, Lecce, Italy, enrico.ciavolino@unisalento.it Abstract In this paper, a new generalization of one parameter Lindely distribution is proposed. The new distribution is a mixture distribution of Gamma distributions with fixed scale parameter and variable shape parameter. The distribution is called ‘GOLD Distribution’ as it is a generalization for several distributions such as exponential, Lindely, Sujatha, Amarendra, Devya and Shambhu distributions. The probability density and cumulative density functions are derived. Also, the statistical properties of the GOLD distribution are discussed. Parameter estimation using the maximum likelihood and the method of moments are given. Moreover, an illustration of the usefulness of the GOLD distribution in survival data analysis is discussed based on a real lifetime data. Key Words: Gamma Distribution, Mixture Distributions, Lindely Distribution, Survival Analysis, Statistical Measures. Mathematical Subject Classification: 46T30, 62N02 1. Introduction Lindely distribution (LD) is one of the most important distribution that is widely used in reliability and survivals data analyses. LD is derived from a two-parameter gamma distribution which is the most popular distribution that is used in analyzing lifetime data. A random variable X is said to have a two-parameter gamma distribution with parameters α (shape parameter) and θ (scale parameter); and denoted by Gamma(α,θ), if its probability density function (pdf) is given by: () = −1 Γ() −/ , > 0; , > 0. It worth to say that, there is no close form for the gamma cumulative distribution function ( cdf), and can be written based on the incomplete gamma function as: () = 1 Γ() Γ (, ), where, Γ(, ) = ∫ −1 − ∞ . However, when has only integer values, then the distribution is known as Erlang distribution and the cdf can be obtained as: () = 1 − ∑ Γ() − −1 =1 , Based on this fact, Lindely (1958) proposed a compound distribution of two independent gamma distributions of the same scale parameters but with different shape parameters with pdf: Pakistan Journal of Statistics and Operation Research