Journal of Data Science ›› 2020, Vol. 18 ›› Issue (2): 279-298.doi: 10.6339/JDS.202004_18(2).0004

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Zografos Balakrishnan Power Lindley Distriution

Noor Shahid1, Rashida khalil2 and Javeria Khokhar3   

  1. 1,2,3 Department of Statistics, Lahore College for Women University Lahore, Pakistan.
  • Online:2020-04-15 Published:2020-05-10

Abstract: In this paper Zografos Balakrishnan Power Lindley (ZB-PL) distribution has been obtained through the generalization of Power Lindley distribution using Zografos and Balakrishnan (2009) technique. For this technique, density of upper record values exists as their special case. Probability density (pdf), cumulative distribution (cdf) and hazard rate function (hrf) of the proposed distribution are obtained. The probability density and cumulative distribution function are expanded as linear combination of the density and distribution function of Exponentiated Power Lindley (EPL) distribution. This expansion is further used to study different properties of the new distribution. Some mathematical and statistical properties such as asymptotes, quantile function, moments, mgf, mean deviation, renyi entropy and reliability are also discussed. Probability density (pdf), cumulative distribution (cdf) and hazard rate (hrf) functions are graphically presented for different values of the parameters. In the end Maximum Likelihood Method is used to estimate the unknown parameters and application to a real data set is provided a. It has been observed that the proposed distribution provides superior fit than many useful distributions for given data set.

Key words: Gamma distribution, Upper record values density function, Power Lindley, Exponentiated Power Lindley, Maximum likelihood estimate