Abstract
In this paper, we introduce a new class of Weighted Rayleigh Distribution based on two parameters, one is the scale parameter and the other is the shape parameter introduced in Rayleigh distribution. The main properties of this class are derived and investigated . The moment method and least square method are used to obtain estimators of parameters of this distribution. The probability density function, survival function, cumulative distribution and hazard function are derived and found. Real data sets are collected to investigate two methods that depend on in this study. A comparison is made between two methods of estimation and clarifies that MLE method is better than the OLS method by using the mean squares error.
Highlights
The Rayleigh distribution is one of the important continuous distributions; it encounters much attention in the literature in benefit from any other distribution in lifetime sample modeling and data analysis
We find that the death density function is increasing with the failure times until (0.074984) when t=11, the values decreasing with failure times from (0.073266) when t=12 until the end of failure times .We find that the survival function is decreasing with the increasing of failure times .We find that the hazard function is increasing with increasing failure times
In the two estimation methods above, the probability estimation values of the survival function are decreasing with the increase in failure time values
Summary
The Rayleigh distribution is one of the important continuous distributions; it encounters much attention in the literature in benefit from any other distribution in lifetime sample modeling and data analysis. Studied the skew-ness parameter of a gamma distribution by using the idea of Azzalini that resulted a new class of weighted gamma distribution.[5] proposed the extension of the weighted Weibull distribution and the main properties of this class are investigated and derived [6]. Proposed a new class of weighted Rayleigh distribution by using the idea of Azzalini and introduce the main characteristics of this distribution.This paper aimsto introduce a new weighted Rayleigh distribution with its properties which discussed maintained in[13] Applying this new distribution on real data to estimate the parameters by using two methods and calculate the death density function, survival function, hazard function for these two methods. The rest of this article is as follows: in section two, the new weighted Rayleigh distribution and its properties is presented, section three xplains estimation methods, in section four is devoted to the real data application and section five gives the conclusion
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