A General Transmuted Family of Distributions

Abstract

In this article we have proposed a general transmuted family of distributions with emphasis on the cubic transmuted (CT) family of distributions. This new class of distributions provide additional flexibility in modeling the bi-modal data. The proposed cubic transmuted family of distributions has been linked with the T − X family of distributions proposed by Alzaatreh et al. (2013). Some members of the proposed family of distributions have been discussed. The cubic transmuted exponential distribution has been discussed in detail and various statistical properties of the distribution have been explored. The maximum likelihood estimation for parameters of cubic transmuted exponential distribution has also been discussed alongside Monte Carlo simulation study to assess the performance of the estimation procedure. Finally, the cubic transmuted exponential distribution has been fitted to real datasets to investigate it's applicability.

Cubic Transmuted Uniform Distribution: An Alternative to Beta and Kumaraswamy Distributions

“…We will now propose some CT U distributions by using the cubic transmuted families proposed by Rahman et al [13,14] and by using (2). These distributions are obtained in the following section.…”

“…The transmutation approach (1) captures the quadratic behavior in the data. Rahman et al [13,14] have extended the transmuted family of distributions, given in (1), by introducing two cubic transmuted families of distributions for any base distribution. In this article, we have proposed a new cubic transmuted family of distributions and have linked it both with the distribution of order statistics and with the T − X family of distributions.…”

“…The rest of the paper is organized as follows: The new family of cubic transmuted distributions is proposed in Section 2. In Section 3, cubic transmuted uniform distributions are proposed by using existing families, as given by Rahman et al [13,14], and by using a new family. In Section 4, statistical properties of the cubic transmuted uniform distribution, obtained by using the new family, are given.…”

Cubic Transmuted Gompertz Distribution: As a Life Time Distribution

“…The Topp-Leone-G family of distribution was introduced by Rezaie et al [5]. Granzotto et al [6] Aslam Mohammad et al [7], Rahman et al [8] studied the Generalized Cubic Transmuted G-distribution using different approaches that found it root from The Generalised transmuted family of distribution by Shaw et al [9]. This work generalize the Gompertz distribution using the generalized Cubic Transmuted-G distribution to impute flexibility and tractability into the Gompertz distribution.…”

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In this work, we proposed and studied the Cubic Transmuted Gompertz (CTG) distribution using the Cubic Transmuted family of distributions which was introduced by Rahman et al [8] and based on cubic transmutation map. We studied the statistical properties of the new distribution which includes: moment, moment generating function order statistics, mean, variance, Renyl entropy.

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