Abstract
In this article, it is interesting to estimate and derive the three parameters which contain two scales parameters and one shape parameter of a new mixture distribution for the singly type one censored data which is the branch of right censored sample. Then to define some special mathematical and statistical properties for this new mixture distribution which is considered one of the continuous distributions characterized by its flexibility. Next, using maximum likelihood estimator method for singly type one censored data based on the Newton-Raphson matrix procedure to find and estimate values of these three parameter by utilizing the real data taken from the National Center for Research and Treatment of Hematology/University of Mustansiriyah for leukemia diseases. After that we find and derive the estimate of probability density function, estimate survival function and finally estimate the hazard function.
Highlights
A new proposed distribution was introduced by the researchers Iden and Maysaa, in (2018) [1] which they called “new mixture distribution”
The new mixture distribution depended on three parts, the first part was a mixture between exponential and standard Weibull distributions, the second part was a mixture between exponential and Rayleigh distributions, and the third part was a mixture between the first part and the second .This distribution was characterized by a flexible distribution and was based on three parameter α, β, γ two of them were scale parameters γ, β and one shape parameter α
This study is based on samples and real data taken from the National Center For Research and Treatment Of Hematology/University of Mustansiriya of chronic lymphocytic leukemia which is one type of leukemia cancers that effects people from aged 60-80 years which is symbolized (CLL)
Summary
A new proposed distribution was introduced by the researchers Iden and Maysaa, in (2018) [1] which they called “new mixture distribution”. Reference was made to the previous paper ,which was based on the same idea G.M. Cordeiro et al, in(2014)[5] that represented the new method to find the mixed distribution depending on tail of Exponential one parameter distribution and Weibull two parameters distribution. Suleman.N in (2016)[4] introduced the new distribution depend on the tail of Weibull two parameters distribution and Rayleigh one parameter distribution. The aim of this paper is to estimate the values of unknown parameters for the new mixed distribution (NMD) based on censored data (type- one censored sample). To estimate the death density function, survival function and hazard function
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