J. Stat. Appl. Pro. 5, No. 2, 1-11 (2017) 1 Journal of Statistics Applications & Probability An International Journal http://dx.doi.org/10.18576/jsap/paper Transmuted Janardan Distribution: A Generalization of the Janardan Distribution Amer Ibrahim Al-Omari * , Ahmed M. H. Al-khazaleh and Loai M. Alzoubi Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq 25113, Jordan Received: 27 Sep. 2016, Revised: 9 Nov. 2016, Accepted: 13 Nov. 2016 Published online: 1 Jul. 2017 Abstract: In this paper, a continuous distribution so-called transmuted Janardan distribution (TJD) is suggested and studied. The quadratic rank transmutation map suggested by Shaw and Buckley (2009) is used in generating the TJD. Various structural properties of the TJD including explicit expressions for the reliability and hazard rate functions, order statistics, the rth moment and the moment generating function are derived. Also, the skewness, kurtosis, coefficient of variation are derived and calculated for some values of the TJD parameters. The maximum likelihood method is used to estimate the unknown parameters of the TJD for complete sample and the entropy is studied and proved. Keywords: Transmuted Janardan distribution, Moments, Entropy, Order statistics. 1 Introduction [1] suggested the transmutation map method, which is used to derive a new model as a generalization of the Janardan Distribution. The new distribution is called the transmuted Janardan distribution (TJD). The transmuted quasi Lindley distribution is obtained by [2]. The transmuted Gumbel distribution and its application in climate data is suggested by [3]. [4] suggested transmuted Two-Parameter Lindley distribution. [5] suggested transmuted exponentiated Frechet distribution. [6] introduced transmuted exponentiated inverse Rayleigh distribution. [7] proposed transmuted exponentiated gamma distribution as a generalization of the exponentiated gamma probability distribution. [8] proposed transmuted exponential-Weibull distribution with some applications. [9] proposed transmuted inverse Rayleigh distribution as a modification of the inverse Rayleigh distribution. The cumulative distribution function (cdf) technique based on the quadratic rank transmutation map satisfies the following general form Φ 2 (x)=(1 + λ )Φ 1 (x) - λ [Φ 1 (x)] 2 , (1) with pdf given by ψ 2 (x)= ψ 1 (x)[1 + λ - 2λΦ 1 (x)], -1 ≤ λ ≤ 1, (2) where ψ 1 (x) and ψ 2 (x) are the corresponding probability density functions (pdf) of Φ 1 (x) and Φ 2 (x), respectively. Note that at λ = 0 , we have ψ 1 (x)= ψ 2 (x) . Definition: A random variable X is said to have a transmuted probability distribution with cdf Φ (x) if Φ (x)=(1 + λ )G(x) - λ [ G(x)] 2 , |λ |≤ 1, (3) where G(x) is the cdf of the base distribution. The rest of this paper is organized as follows: In Section 2 we demonstrate the pdf and cdf of the transmuted Janardan distribution. The reliability and hazard rate functions of the subject model are presented in Section 3. In Section 4, the distributions of order statistics are summarized. In Section 5, the statistical properties including the rth moment, variance, * Corresponding author e-mail: alomari amer@yahoo.com c  2017 NSP Natural Sciences Publishing Cor.