Exponentiated generalized linear exponential distribution

Sarhan, Ammar M.; Ahmad, Abd EL-Baset A.; Alasbahi, Ibtesam A.

doi:10.1016/j.apm.2012.06.019

Cited by 38 publications

(30 citation statements)

References 10 publications

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“…For comparison, we fitted the first data set with the following distributions, the POGE-HL, POE-HL, odd generalized exponential half logistic (OGE-HL), Poisson half logistic (PHL) by [2], exponentiated half logistic (EHL) by [15], Olapade-generalized half logistic (OLGHL) by [32], generalized exponential (GE) by [14], generalized exponential Poisson (GEP) by [8], BurrXII-Poisson (BXIIP) by [38] and generalized BurrXII-Poisson (GBXIIP) by [28]. For the second data we fitted the POGE-U distribution and compare the fit with the POE-U, odd generalized exponential uniform (OGE-U), gamma-uniform (GU) by [41], generalized modified weibull (GMW) by [11], beta modified weibull (BMW) by [36], beta weibull (BW) by [18], modified weibull distribution (MW) by [17], generalized linear failure rate (GLFR) by [35], generalized linear exponential (GLE) by [20], exponentiated generalized linear exponential (EGLE) by [34] and some family of the generalized modified weibull-power series (GMWPS) such as generalized modified weibull-Poisson (GMWP), generalized modified weibull-Geometric (GMWG) and generalized modified weibull-Logarithmic (GMWL) distributions proposed by [5]. The MLEs of the parameters for each model are computed and the three criteria for model selection are used for comparison namely the Akaike information criterion (AIC), consistent Akaike information criterion (CAIC) and Bayesian information criterion, also the goodness-of-fit statistics known as the Kolmogorov Smirnov (KS) is used to compare the fit of the new POGE family and other competing models.…”

Section: Applicationmentioning

confidence: 99%

“…In probability modeling, numerous families of distributions have been proposed and studied via different directions based on the exponential distribution. For instance, some distributions generalized (or extended) the exponential distribution, these includes the Weibull (W) distribution, linear failure rate distribution (LFR), generalized exponential distribution (GE) by [14], generalized linear failure rate (GLFR) by [35], generalized linear exponential (GLE) by [20], exponentiated generalized linear exponential (EGLE) by [34], the Nadarajah and Haghighi's (NHE) exponential-type by [29], among other.…”

Section: Introductionmentioning

confidence: 99%

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Poisson-odd generalized exponential family of distributions: Theory and Applications

Muhammad¹

2016

HJMS

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In this paper, we introduce a new family of distributions called the Poisson-odd generalized exponential distribution (POGE). Various properties of the new model are derived and studied. The new distribution has the odd generalized exponential as its limiting distribution. We present and study two special cases of the POGE family of distributions, namely the Poisson odd generalized exponential-half logistic and the Poisson odd generalized exponential-uniform distributions. Estimation and inference procedure for the parameters of the new distribution are discussed by the method of maximum likelihood; we also evaluate the proposed estimation method by simulation studies. Applications to two real data sets are provided in order to demonstrate the performance of the proposed family of distributions.

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Section: Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Poisson-odd generalized exponential family of distributions: Theory and Applications

Muhammad¹

2016

HJMS

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“…Linear-exponential distribution function is a commonly used probability distribution for modeling lifetime data and also phenomenon with linearly increasing failure rates [17]. Exponential and Rayleigh distributions are known as sub-models of linear exponential distribution function [10,17].…”

Section: Introductionmentioning

confidence: 99%

“…For this purpose, different distribution functions, such as normal, lognormal, Weibull, exponential and linear-exponential distribution functions, have been considered in the literature to improve system reliability [10,12,16,17].…”

Section: Introductionmentioning

confidence: 99%

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Evaluating system reliability using linear-exponential distribution function

Ezzati¹,

Rasouli²

2014

IJASP

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Safety is a main criterion to design every system. Among various theories, which are applied to improve system safety, reliability theory is known as a powerful tool to reach higher safety levels in system design. In this paper, a compound of series and parallel systems is considered for reliability improvement. This system includes three items that two items are connected in parallel and their compound item is connected to the third item in series. It's assumed that the items are independent and their longevity follows linear-exponential distribution function. Reliability function of the mentioned system is formulated using linear-exponential distribution function. Then, three improvement methods will be applied to enhance system reliability. In each method, different sets of items will be considered for improvement and their reliability functions will be reformulated. A data analysis will be done in order to compare different improvement methods and a conclusion will be made based on the analyzed data.

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Further theories on application of new generalized probability density function and its applications

Erem

Bilgehan²,

Özyapıcı

et al. 2022

Quality & Reliability Eng

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The exponential‐based probability density functions (PDFs) such as Gaussian, exponential, and Rayleigh are widely used in lifetime modeling, survival analysis, and engineering. Recently, the generalized probability density functions consisting a well‐known exponential PDFs were introduced and successfully applied in electrical and electronic engineering. After encouraging results of generalized PDF, further theories and applications are considered within this paper. The parameters of the new (GE) PDF were successfully derived by using the maximum likelihood estimation method. The applications in the paper show that the new generalized probability density function based on maximum likelihood parameter estimators provides more effective probabilistic representation. In this study, statistical properties of new GE distribution is discussed. Some reliability characteristics such as hazard function, mean residual lifetime (MRL) function, and mean past lifetime (MPL) functions are obtained based on special functions. Also, r$r$th moment of the new GE random variable is obtained in analytical form. Maximum likelihood estimates (MLEs) of parameters are also discussed. Lastly, some illustrative examples in engineering and survival analysis are provided based on different real data sets.

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Exponentiated generalized linear exponential distribution

Cited by 38 publications

References 10 publications

Poisson-odd generalized exponential family of distributions: Theory and Applications

Poisson-odd generalized exponential family of distributions: Theory and Applications

Evaluating system reliability using linear-exponential distribution function

Further theories on application of new generalized probability density function and its applications

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