Abstract
Finding the best fitted distribution for data set becomes practically an important problem in world of data sets so that it is useful to use new families of distributions to fit more cases or get better fits than before. In this paper, a new generating family of generalized distributions so called the Kumaraswamy - Kumaraswamy (KW-KW) family is presented. Four important common families of distributions are illustrated as special cases from the KW KW family. Moments, probability weighted moments, moment generating function, quantile function, median, mean deviation, order statistics and moments of order statistics are obtained. Parameters estimation and variance covariance matrix are computed using maximum likelihood method. A real data set is used to illustrate the potentiality of the KW KW weibull distribution (which derived from the kw kw family) compared with other distributions.
Highlights
The main idea of this paper is based on generating new families of generalized distributions, see Wahed (2006), to derive more generalized distributions from the following integration G1 x ; WF (x ; T,W ) g 2 (t ;T) dt ;0 t 1; x (1)Where G1(x ;W ) and g1(x ;W ) are the cdf and pdf of the baseline distribution, G2 (t ; T )and g 2 (t ; T ) are the cdf and the pdf of the generator distribution, T is the parameters vector of the generator distribution and W is the parameters vector of the baseline distribution.The contributions of this paper are four parts
We calculate some properties of KW KW family like Moments, probability weighted moments, moment generating function, quantile function, median, mean deviation, order statistics and moments of order statistics
In Table (2) and based on the likelihood ratio test, where the KW- kumaraswamy weibull (KW-W) (a, b, α, β, θ, λ) distribution generalizes the exponentiated kumaraswamy weibull (E-KW-W) (a, α, β, θ, λ) distribution, the KW -W (α, β, θ, λ) distribution, the EG -W (a, β, θ, λ) distribution, the exponentiated weibull (E-W) (α, θ, λ) distribution, the E-W (α, θ, λ) distribution and the W(θ, λ) distribution, we find from the p-values that we can reject all null hypotheses when the level of significance is 0.1
Summary
The main idea of this paper is based on generating new families of generalized distributions, see Wahed (2006), to derive more generalized distributions from the following integration. Where G1(x ;W ) and g1(x ;W ) are the cdf and pdf of the baseline distribution, G2 (t ; T ). G 2 (t ; T ) are the cdf and the pdf of the generator distribution, T is the parameters vector of the generator distribution and W is the parameters vector of the baseline distribution. We present the pdf and cdf of the new KW KW family of generalized distributions (section 2). We calculate some properties of KW KW family like Moments, probability weighted moments, moment generating function, quantile function, median, mean deviation, order statistics and moments of order statistics (section 3). We present a numerical example using real data on the KW KW Weibull and it gives the best fit between other distributions (section 5)
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