Burhan Distribution with Structural Properties and Applications in Distinct Areas of Science

Abstract

In this work a novel distribution has been explored referred as Burhan distribution. This distribution is obtained through convex combination of exponential and gamma distribution to analyse complex real-life data. The distinct structural properties of the formulated distribution have been derived and discussed. The behaviour of probability density function (pdf) and cumulative distribution function (cdf) are illustrated through different graphs. The estimation of the established distribution parameters are performed by maximum likelihood estimation method. Eventually the versatility of the established distribution is examined through two real life data sets.

Quartic Rank Transmuted Gumbel Distribution

“…where w = e −( x−µ σ ) , σ > 0, µ ∈ R. and G(X; µ, σ) = e −w ; x ∈ R (2) Some extensions of the Gumbel distribution have previously been proposed. The Beta Gumbel distribution,(Nadarajah et al [13]), the Exponentiated Gumbel distribution as a generalization of the standard Gumbel distribution introduced by Nadarajah [12],and the Exponentiated Gumbel type-2 distribution, studied by Okorie et al [14], Transmuted Gumbel type-II distributton with applications in diverse fields of science by Ahmad et al [1], giving Transmuted exponentiated Gumbel distribution (TEGD) and its application to water quality data of Deka et al [7], and transmuted Gumbel distribution (TGD) along with several mathematical properties has studied by Aryal and Tsokos [4] using quadratic rank transmutation. Quadratic rank transmuted distribution has been proposed by Shaw and Buckley [18].…”

The Cubic Rank Transmuted Gumbel Distribution

“…Nadarajah et al [13] Submitted The Beta Gumbel distribution, Nadarajah [12] developed the Exponentiated Gumbel distribution as a generalization of the basic Gumbel distribution. Considering the distribution of Exponentiated Gumbel type-2, which was investigated by Okorie et al [14], transmuted Gumbel type-II distribution, which has applicability in many different scientific domains by Ahmad et al [1], giving Deka et al [6], Transmuted exponentiated Gumbel distribution (TEGD) and its application to water quality data, Aryal and Tsokos [3] used quadratic rank transmutation to investigate the transmuted Gumbel distribution (TGD) as well as numerous mathematical features. Shaw and Buckley [18] proposed a quadratic rank transmuted distribution.…”