© 2018, IJCSE All Rights Reserved 25 International Journal of Scientific Research in _______________________________ Research Paper . Mathematical and Statistical Sciences Volume-5, Issue-5, pp.25-32, October (2018) E-ISSN: 2348-4519 Transmuted Generalized Uniform Distribution C. Subramanian 1 and A. A. Rather 2 1,2 Department of Statistics, Annamalai University, Annamalai Nagar, Tamil Nadu, India 2 Corresponding Author: aafaq7741@gmail.com Available online at: www.isroset.org Received: 19/Sept/2018, Accepted: 12/Oct/2018, Online: 31/Oct/2018 Abstract-In this paper we have introduced a new probability model called as transmuted generalized Uniform distribution (TGUD) by using the quadratic rank transmutation map studied by Shaw and Buckley (2007). The moments, survival function, failure rate and reverse hazard rate of the distribution have been derived. The parameters have been estimated by the maximum likelihood method. Also we have obtained the pdf of r th , 1 st and n th order statistics. Keywords: Transmuted generalized Uniform distribution, Moments, Reliability analysis, Parameter estimation, Order statistics I. INTRODUCTION Statistics is the science of drawing inferences about random phenomena in which chances play an important role. Transmuted distributions have been discussed dynamically in frequently occurring large scale experimental statistical data for model selection and related issues. A significant progress has been made towards the generalization of some well known distributions. These extended distributions find their application in many lifetime problems like medical, economics, finance, environmental, engineering and biomedical sciences. There are several distributions which can be used to model such kind of experimental data. The procedures used in such a statistical analysis depend heavily on the assumed probability model or distributions. That is why the development of large classes of standard probability distributions along with relevant statistical methodologies has been expanded. However, there still remain many important problems where the real data does not follow any of the classical or standard probability models. Shaw and Buckley (2007) introduced the new quadratic rank transmutation map (QRTM) technique. The quadratic rank transmutation map, will be used in this paper to derive a generalization of the Generalized Uniform distribution. This generalization is termed as Transmuted Generalized Uniform distribution (TGUD). Generally, transmutation maps are a convenient way of constructing new distributions, in particular, survival ones. Aryal and Tsokos (2009) discussed on the transmuted extreme value distribution. Afify et al. (2015) discussed transmuted weibull lomax distribution. Deepshikha et al. (2017) also discussed on transmuted exponential gumbel distribution and its applications to water quality data. Recently, Rather and Subramanian (2018) obtained a new transmuted mukherjee-islam failure model which shows more flexibility than classical distributions. A probability distribution can be characterized through various methods. Generalized uniform distribution is characterized through the conditional expectation of lower record values. Ali et al. (2007), study a new property exponentiated generalized uniform distribution. Bhatt (2014), discussed characterization of generalized uniform distribution through expectation. Khan and khan (2017), obtained the characterization of generalized uniform distribution based on lower record values. According to quadratic rank transmutation map (QRTM) technique approach, a random variable X is said to have a Transmuted distribution, if its cdf is given by   ] ) ( ) ( ) 1 [( ) ( 2 x G x G x F      1   (1) Where G(x) is the cdf of the base distribution and F(x) is the cdf of Transmuted distribution. Differentiating (1) with respect to x, we will get the pdf of Transmuted distribution as   ) ( 2 1 ) ( ) ( x G x g x f      (2)