TRANSMUTED GUMBEL UNIVARIATE EXPONENTIAL DISTRIBUTION

Hameldarbandi, Monireh; Yılmaz, MEHMET

doi:10.31801/cfsuasmas.567496

TRANSMUTED GUMBEL UNIVARIATE EXPONENTIAL DISTRIBUTION

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.69, sa.1, ss.137-157, 2020 (ESCI)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 69 Sayı: 1
Basım Tarihi: 2020
Doi Numarası: 10.31801/cfsuasmas.567496
Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
Sayfa Sayıları: ss.137-157
Anahtar Kelimeler: Gumbel exponential distribution, convex combination, transmutation method, hazard rate function, exponential distribution
Ankara Üniversitesi Adresli: Evet

Özet

A functional composition of the distribution function of one probability distribution with the inverse distribution function of another is called the transmutation map. The present paper is purported to show how the transmuted distribution can be obtained by using the convex combination of failure probability of two-component systems. The transmuted Gumbel univariate exponential distribution is presented by changing convex combination parameter. This new distribution is defined and studied. Some mathematical properties of this distribution including the generating function and ordinary moments are derived. The survival, hazard rate and mean residual life functions are discussed. Finally, three applications to real data are presented.