Abstract
In this paper, an estimate has been made for parameters and the reliability function for Transmuted power function (TPF) distribution through using some estimation methods as proposed new technique for white, percentile, least square, weighted least square and modification moment methods. A simulation was used to generate random data that follow the (TPF) distribution on three experiments (E1 , E2 , E3) of the real values of the parameters, and with sample size (n=10,25,50 and 100) and iteration samples (N=1000), and taking reliability times (0< t < 0) . Comparisons have been made between the obtained results from the estimators using mean square error (MSE). The results showed the percentile estimator is the best in (E1, E2) but modification moment is the best in (E3) .
Highlights
The power function (PF) distribution is one of the distributions derived from the beta distribution, many researchers have studied this distribution by estimating its parameters and the reliability function because it is one of the distributions used in reliability .The probability density function and the cumulative distribution function with scale parameter θ > 0 and shape parameter α > 0 are given, respectively, as follows 1: g(x; α, θ)
White estimation method depends mainly on its application on the reliability function of distribution 4, a new technique is proposed for white method which depends on the cumulative distribution function. for estimating its parameters and format conversion function to formulate similar linear regression equation, which is characterized by the use of its estimate as an initial value of the other estimation methods, from (1), getting : α θα 1 + λ 2
A new technique is proposed for white estimation method, and it has presented good estimators for scale parameters and reliability function
Summary
For estimating its parameters and format conversion function to formulate similar linear regression equation, which is characterized by the use of its estimate as an initial value of the other estimation methods, from (1), getting : α θα 1 + λ 2 Parameters estimation for this method depends on inverse distribution function for any distribution. To find estimation formulas for (θ) and (α), taking the partial derivative of (17) w.r.t (θ) and (α) and equating to zero, respectively, getting:
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