An alternative for Laplace Birnbaum-Saunders distribution

BİRBİÇER İ., Genc A. İ.

MATHEMATICA SLOVACA, cilt.72, sa.4, ss.1063-1090, 2022 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 72 Sayı: 4
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1515/ms-2022-0074
  • Dergi Adı: MATHEMATICA SLOVACA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.1063-1090
  • Anahtar Kelimeler: Lifetime distribution, triangular distribution, two-piece distribution, existence and uniqueness of maximum likelihood estimates, PARAMETERS, UNIQUENESS, EXISTENCE, FAMILY
  • Çukurova Üniversitesi Adresli: Evet

Özet

In this paper, we first propose a new general method to introduce various lifetime distributions by choosing an appropriate kernel distribution. They have some characteristics in common with the well-known Birnbaum-Saunders distribution. Then, we choose the triangular distribution as a kernel model and construct the new distribution. This distribution has its support on the positive real axis and consists of two-pieces. We show that the newly defined distribution is in fact a generalized Birnbaum-Saunders distribution. It is mathematically tractable for studying its theoretical properties in detail. Different methods of estimation of parameters are proposed. The existence and uniqueness problem of the maximum likelihood estimation method is discussed. The performances of the estimators are evaluated through simulation studies. A real data fitting which compares it with the ordinary Birnbaum-Saunders, Laplace Birnbaum-Saunders and other some generalized Birnbaum-Saunders distributions is also given.