Mathematics and Statistics Vol. 11(2), pp. 308 - 314
DOI: 10.13189/ms.2023.110209
Reprint (PDF) (481Kb)

Exponential-Inverse Exponential[Weibull]: A New Distribution

Mahmoud Riad Mahmoud ¹, Azza E. Ismail ^1,*, Moshera A. M. Ahmad ^2
1 Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, Egypt
² El Gazeera High Institute for Computer & Management Information System, Egypt

ABSTRACT

Statistical distributions play a major role in analyzing experimental data, and finding an appropriate one for the data at hand is not an easy task. Extending a known family of distribution to construct a new one is a long honored technique in this regard. The T-X[Y] methodology is utilized to construct a new distribution as described in this study. The T-inverse exponential family of distributions, which was previously introduced by the same authors, is used to examine the exponential-inverse exponential[Weibull] distribution (Exp-IE[Weibull]). Several fundamental properties are explored, including survival function, hazard function, quantile function, median, skewness, kurtosis, moments, Shannon’s entropy, and order statistics. Our distribution exhibits a wide range of shapes with varying skewness and assume most possible forms of hazard rate function. The unknown parameters of the Exp-IE [Weibull] distribution are estimated via the maximum likelihood method for a complete and type II censored samples. We performed two applications on real data. The first one is vinyle chloride data, which is explained by [1] and the second is cancer patients data, which is explained by [2]. The significance of the Exp-IE[Weibull] model in relation to alternative distributions (Fr´echet, Weibull-exponential, logistic-exponential, logistic modified Weibull, Weibull-Lomax [log-logistic] and inverse power logistic exponential) is demonstrated. When using the applied real data, the new distribution (Exp-IE[Weibull]) achieved better results for the AIC and BIC criterion compared to other listed distributions.

KEYWORDS
Quantile Function, Shannon’s Entropy, T-X[Y] Framework, T-IE Family

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Mahmoud Riad Mahmoud , Azza E. Ismail , Moshera A. M. Ahmad , "Exponential-Inverse Exponential[Weibull]: A New Distribution," Mathematics and Statistics, Vol. 11, No. 2, pp. 308 - 314, 2023. DOI: 10.13189/ms.2023.110209.

(b). APA Format:
Mahmoud Riad Mahmoud , Azza E. Ismail , Moshera A. M. Ahmad (2023). Exponential-Inverse Exponential[Weibull]: A New Distribution. Mathematics and Statistics, 11(2), 308 - 314. DOI: 10.13189/ms.2023.110209.