TY - JOUR
T1 - The Marshall-Olkin logistic-exponential distribution
AU - Mansoor, M.
AU - Tahir, M. H.
AU - Cordeiro, Gauss M.
AU - Provost, Serge B.
AU - Yousef Abdelfattah Alzaatreh, Ayman
PY - 2018/1/4
Y1 - 2018/1/4
N2 - We introduce a three-parameter extension of the exponential distribution which contains as sub-models the exponential, logistic-exponential and Marshall-Olkin exponential distributions. The new model is very flexible and its associated density function can be decreasing or unimodal. Further, it can produce all of the four major shapes of the hazard rate, that is, increasing, decreasing, bathtub and upside-down bathtub. Given that closed-form expressions are available for the survival and hazard rate functions, the new distribution is quite tractable. It can be used to analyze various types of observations including censored data. Computable representations of the quantile function, ordinary and incomplete moments, generating function and probability density function of order statistics are obtained. The maximum likelihood method is utilized to estimate the model parameters. A simulation study is carried out to assess the performance of the maximum likelihood estimators. Two actual data sets are used to illustrate the applicability of the proposed model.
AB - We introduce a three-parameter extension of the exponential distribution which contains as sub-models the exponential, logistic-exponential and Marshall-Olkin exponential distributions. The new model is very flexible and its associated density function can be decreasing or unimodal. Further, it can produce all of the four major shapes of the hazard rate, that is, increasing, decreasing, bathtub and upside-down bathtub. Given that closed-form expressions are available for the survival and hazard rate functions, the new distribution is quite tractable. It can be used to analyze various types of observations including censored data. Computable representations of the quantile function, ordinary and incomplete moments, generating function and probability density function of order statistics are obtained. The maximum likelihood method is utilized to estimate the model parameters. A simulation study is carried out to assess the performance of the maximum likelihood estimators. Two actual data sets are used to illustrate the applicability of the proposed model.
KW - Censored data
KW - Logistic distribution
KW - Logistic-exponential distribution
KW - Marshall-Olkin family
KW - Maximum likelihood estimation
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U2 - 10.1080/03610926.2017.1414254
DO - 10.1080/03610926.2017.1414254
M3 - Article
AN - SCOPUS:85041122656
SP - 1
EP - 15
JO - Communications in Statistics - Theory and Methods
JF - Communications in Statistics - Theory and Methods
SN - 0361-0926
ER -