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ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS (Issues…
ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS
Issues Discussed
Importance of exponential distribution in engineering field
Failure rate of an equipment; either more or less constant
Parameters
Gamma = Guarantee rate
Beta = Failure rate
Problem Statement
Exponential distribution parameters portrays the lifetime of industrial equipment
Mean Square Error (MSE)
Total Deviation (TD)
Estimation of parameter
Location
Interval: greater than or equal to zero
Scale
Interval: more than zero
Methodology
Comparing accuracy of estimators using Mean Square Error &Total Deviation
Relative Least Squares Method
Moment Estimator
Ridge Regression Method
First-Modified Moment Estimators
Second Modified Moment Estimators
Third Modified Moment Estimators
Maximum Likehood Estimator
First Modified Maximum Likelihood Estimator
Least Square Method
Analysis Conducted
Compare the capability of different estimation methods using different sample sizes
Sample Sizes: 20, 40, 60, 80, 100
Parameters (Gamma, Beta): (1,1), (1,2), (2,3)
Outcome of Analysis & Conclusion
Suggested third modified moment estimator & first modified maximum likelihood estimator as both give better accuracy compared to their original form
Least Square Method produce the closest true value and a very small MSE & TD for the estimate of parameter