Abstract
The two parameter Burr type X distribution is considered and its scale parameter is estimated from a censored sample using the classical maximum likelihood method. The estimating equations are modified to get simpler and efficient estimators. Two methods of modification are suggested. The small sample efficiencies are presented.
Highlights
In reliability studies exponential distribution is the central model for the study of any phenomenon through a probabilistic approach
The Weibull distribution is more frequently applied model in any practical situation concerning reliability studies. Both Weibull and gamma distributions involve a shape parameter, in the sense that the shape of the frequency curve of these models changes according as the change in the values of the shape parameters
For the Weibull distribution its shape parameter classifies it into an Increasing Failure Rate (IFR) model or a Decreasing Failure Rate (DFR) model or Constant Failure Rate (CFR) model as its special cases
Summary
In reliability studies exponential distribution is the central model for the study of any phenomenon through a probabilistic approach. Extension of this model into two different directions yields two popular models called the Weibull distribution and the gamma distribution Between these two, the Weibull distribution is more frequently applied model in any practical situation concerning reliability studies. The Weibull distribution is more frequently applied model in any practical situation concerning reliability studies Both Weibull and gamma distributions involve a shape parameter, in the sense that the shape of the frequency curve of these models changes according as the change in the values of the shape parameters. Ravikumar a parallel system of k- components whose life times are independently and identically distributed random variables, each with a common CDF – F(x) if k is an integer Exploring this concept to non integer values of k many researchers in the recent past made extensive studies on models of the type [ ( )] generated by a basic well known model F(x). As these processes involve a lot of numerical computations, we present our results in the forms various numerical tables towards the end of respective sections of this paper with the respective labels of identification
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