The Additive Weibull-Geometric Distribution: Theory and Applications

Abstract

In this paper, we introduce a new class of lifetime distributions which is called the additive Weibull geometric (AWG) distribution. This distribution obtained by compounding the additive Weibull and geometric distributions.The new distribution has a number of well-known lifetime special sub-models such as modified Weibull geometric, Weibull geometric, exponential geometric, among several others. Some structural properties of the proposed new distribution are discussed. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

A New Family of Lifetime Models: Theoretical Developments with Applications in Biomedical and Environmental Data

“…Power outages can also be triggered by wildlife and tree branches hitting power cables. This data set is obtained from [29] the power failures' lengths measured in minutes: 22,18,135,15,90,78,69,98,102,83,55,28,121,120,13,22,124,112,70,66,74,89,103,24,21,112,21,40,98,87,132,115,21,28,43,37,50,96,118,158,74,78,83,93,95. We have also grouped the data with the help of the bins code of the R computational package, where possible classes with respective frequencies are enlisted as [13, 22.7], [22.7, 53.3], [53.3, 78] 20 and 21).…”

“…This phenomenon of adding parameters innovates more robust families of distributions, which are being effectively used for modeling engineering, economics, biological studies and environmental sciences data sets. Therefore, in this regard, some famous classes are the Marshall Olkin-G by [1], beta-G by [2], the Kumaraswamy-G studied by [3], odd Fréchet-G by [4] logistic-G by [5], exponentiated generalized-G proposed by [6], odd generalized N-H-G by [7], T -X class by [8], transmuted odd Fréchet-G by [9], exponentiated power generalized Weibull power series-G by [10], the Weibull-G by [11], the exponentiated half-logistic generated family by [12], Type II half logistic class by the odd [13], bivariate Weibull-G family by [14], exponentiated generalized alpha power family of distributions by [15], truncated Cauchy power Weibull-G class of distributions by [16], odd Perks-G class of distributions by [17], Type I half logistic Burr X-G family by [18], sine Topp-Leone-G family of distributions by [19], exponentiated version of the M family of distributions by [20], a new power Topp-Leone generated family of distributions by [21], truncated inverted Kumaraswamy generated family of distributions by [22], generalized exponential class discussed by [23], the beta odd log-logistic generalized studied by [24], alpha power transformation family of distributions introduced by [25], the Kumaraswamy exponential Pareto proposed by [26], the generalized Burr XII power series(GBXIIPS) class studied by [27], additive Weibull geometric (AWG) distribution proposed by [28] and the beta exponentiated modified Weibull (BEMW) distribution developed by [29], among others. However, in recent years, Ref.…”

Discrete Additive Weibull Geometric Distribution

“…In this section, to show how the DAWG ( p, , , , ) distribution works in practice, we use the data set representing remission times (in months) of 128 bladder cancer patients taken from Lee and Wang [29]. The data are: 0.080 0.200 0.400 0.500 0.510 0.810 0.900 1.050 1 Since the data set is continuous, here first we discretize the data by considering the floor value (y). The parameters are estimated by using the method of MLE.…”

The Chen–Perks Distribution: Properties and Reliability Applications

“…For this, Thach established the triple additive WD, which is an excellent fit to the bathtub curve; however, makes it complex as it has too many parameters to estimate. Other distributions based on the additive methodology can be seen in [17][18][19][20][21][22].…”