ESTIMATION ACCURACY OF EXPONENTIAL DISTRIBUTION PARAMETERS

Issues Discussed

Problem Statement

Methodology

Analysis Conducted

Outcome of Analysis & Conclusion

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

Exponential distribution parameters portrays the lifetime of industrial equipment

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Mean Square Error (MSE)

Total Deviation (TD)

Estimation of parameter

Suggested third modified moment estimator & first modified maximum likelihood estimator as both give better accuracy compared to their original form

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)

Least Square Method

Importance of exponential distribution in engineering field

Failure rate of an equipment; either more or less constant

Location

Scale

Interval: more than zero

Interval: greater than or equal to zero

Parameters

Gamma = Guarantee rate

Beta = Failure rate

Least Square Method produce the closest true value and a very small MSE & TD for the estimate of parameter