A Comparative Analysis on the Performance of the Convoluted Exponential Distribution and the Exponential Distribution in Terms of Flexibility

Owoloko, E. A.; Oguntunde, Pelumi E.; Adejumo, A. O.

doi:10.3844/jmssp.2016.59.64

Cited by 3 publications

(1 citation statement)

References 12 publications

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“…The data were observed and reported in [18]. For previous studies with the data see [19]. The data are as follows: 33, 44, 56, 59, 72, 74, 77, 92, 93, 96, 100, 100, 102, 105, 107, 107, 108, 108, 108, 109, 112, 113, 115, 116, 120, 121, 122, 122, 124, 130, 134, 136, 139, 144, 146, 153, 159, 160, 163, 163, 168, 171, 172, 176, 183, 195,196,197,202,213,215,216,222,230,231,240,245,251,253,254,254,278,293,327,342,347,361,402,432,458,555.…”

Section: Data Setmentioning

confidence: 96%

Transmuted Weibull distribution and its applications

Pobocikova

Michalková

2018

MATEC Web Conf.

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Section: Data Setmentioning

confidence: 96%

Transmuted Weibull distribution and its applications

Pobocikova

Michalková

2018

MATEC Web Conf.

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The Weibull Claim Model: Bivariate Extension, Bayesian, and Maximum Likelihood Estimations

Emam

Tashkandy

2022

Mathematical Problems in Engineering

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Using a class of claim distributions, we introduce the Weibull claim distribution, which is a new extension of the Weibull distribution with three parameters. The maximum likelihood estimation method is used to estimate the three unknown parameters, and the asymptotic confidence intervals and bootstrap confidence intervals are constructed. In addition, we obtained the Bayesian estimates of the unknown parameters of the Weibull claim distribution under the squared error and linear exponential function (LINEX) and the general entropy loss function. Since the Bayes estimators cannot be obtained in closed form, we compute the approximate Bayes estimates via the Markov Chain Monte Carlo (MCMC) procedure. By analyzing the two data sets, the applicability and capabilities of the Weibull claim model are illustrated. The fatigue life of a particular type of Kevlar epoxy strand subjected to a fixed continuous load at a pressure level of 90% until the strand fails data set was analyzed.

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Ordinary differential equations of probability functions of convoluted distributions

Okagbue¹,

Adamu²,

Anake³

2018

Int. j. adv. appl. sci.

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Convolution is the sum of independent and identically distributed random variables. Derivatives of the probability density function (PDF) of probability distribution often lead to the construction of ordinary differential equation whose solution is the PDF of the given distribution. Little have been done to extend the construction of the ODE to the PDF, quantile function (QF), survival function (SF), hazard function (HF) and the reversed hazard function (RHF) of convoluted probability distributions. In this paper, three probability distributions were considered namely: Constant parameter convoluted exponential distribution (CPCED), convoluted uniform exponential distribution (CUED) and different parameter convoluted exponential distribution (DPCED). First order ordinary differential equations whose solutions were the PDF, SF, HF and RHF for the probability functions of CPCED by the use of differential calculus. The case of the QF was second order nonlinear differential equations obtained by the use of Quantile Mechanics. Similarly, the same was obtained for CUED for the two cases of the distribution. Some new relationships were obtained for the PDF, SF and HF, and also the RHF, PDF and CDF with their corresponding first derivatives. The difficulty of obtaining the ODE for the probability functions of the DPCED was due to the different parameters that characterize the distribution. The use of partial different equations is not an alternate because the distribution has only one independent variable.

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A Comparative Analysis on the Performance of the Convoluted Exponential Distribution and the Exponential Distribution in Terms of Flexibility

Cited by 3 publications

References 12 publications

Transmuted Weibull distribution and its applications

Transmuted Weibull distribution and its applications

The Weibull Claim Model: Bivariate Extension, Bayesian, and Maximum Likelihood Estimations

Ordinary differential equations of probability functions of convoluted distributions

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