This paper introduces a general family of continuous distributions, based on the exponential-logarithmic distribution and the odd transformation. It is called the “odd exponential logarithmic family”. We intend to create novel distributions with desired qualities for practical applications, using the unique properties of the exponential-logarithmic distribution as an initial inspiration. Thus, we present some special members of this family that stand out for the versatile shape properties of their corresponding functions. Then, a comprehensive mathematical treatment of the family is provided, including some asymptotic properties, the determination of the quantile function, a useful sum expression of the probability density function, tractable series expressions for the moments, moment generating function, Rényi entropy and Shannon entropy, as well as results on order statistics and stochastic ordering. We estimate the model parameters quite efficiently by the method of maximum likelihood, with discussions on the observed information matrix and a complete simulation study. As a major interest, the odd exponential logarithmic models reveal how to successfully accommodate various kinds of data. This aspect is demonstrated by using three practical data sets, showing that an odd exponential logarithmic model outperforms two strong competitors in terms of data fitting.
In this paper, the applications of the half logistic-Marshall Olkin X family of distributions are investigated with special emphasis to the half logistic-Marshall Olkin Lomax distribution. The specific areas we concentrated are time series modeling, acceptance sampling plan and stress-strength analysis. Different autoregressive minification structures of order one are introduced. The acceptance sampling plan is detailed by considering life time of products following the half logistic-Marshall Olkin Lomax distribution. The stress-strength reliability of the half logistic-Marshall Olkin Lomax distribution is derived and estimated. A simulation study is carried out to examine the bias, mean square error, average confidence length and coverage probability of the maximum likelihood estimator of thestress-strength reliability. Finally a real-life data analysis has also been presented.
ESFII del IPN D e~~~r t r n e r i t of 7 l a t h~m a t i c 5 Edificio 9. U. P. Zacatrnco L71ii~ ersitj-of .A1 izona 07738 114xico. D.F. T~~c w n . Ai7ona 83721 AIESIC'O 1-5 A AbstractIn this paper we introduce and study an extension to the bivariate setting of a model of failures and repairs which \\as studied by Rocha-hlartinpz aud Shaked (1993). 'I\e suppuse that each of two units has a sequence or tasks to perforrn. The units execute sin~ultaneously their corresponding tasks. I:pon a failurc, t,he failed linit may be repaired (\vith some prohal~ilityj alld then it is given another chance tu perfur~r~ its current task. If the repair is riot successful, then the failure is a i d t u be ratal. At earh particular task, if one unit fatally fails and thr other dues not. t h r r~ the live unit continues to perforrrl its tasks. Thc outpl~t lifetimes (of thc. ur~its i n this model arc measured by t.hr numbers of tasks performed hy the units 1~efur.e thc>ir fatal i'ailurrs. TVe fir~d tile distribution of the outpli t Iifc3tilnes. Some c.samples are gi\,en. Finally, we prove two results concerning storh astir comparisons of pairs oC such no deli.
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