A Note on the Approximation of Empirical Critical Values - An Application to Tests of Exponentiality  
  Authors : Mbanefo Madukaife

 

The behaviour of empirical critical values in asymptotic tests for exponentiality with respect to their protection against errors of type I and type II when approximated by exact theoretical values is discussed. Three tests for exponentiality whose statistics are normally distributed are arbitrarily selected for the study. Each of the tests is described. The empirical critical values of the tests are obtained through Monte Carlo computations under different levels of significance and different sample sizes and these values are compared with their corresponding theoretical critical values. The results are discussed and interpreted.

 

Published In : IJCAT Journal Volume 1, Issue 8

Date of Publication : 30 September 2014

Pages : 427 - 431

Figures :--

Tables : 02

Publication Link : A Note on the Approximation of Empirical Critical Values - An Application to Tests of Exponentiality

 

 

 

Mbanefo Madukaife : Department of Statistics, University of Nigeria, Nsukka Nsukka, Enugu State, Nigeria

 

 

 

 

 

 

 

Empirical Critical Value

Goodness - of - Fit Test

Monte Carlo Simulation

Test for Exponentiality

Type I Error

Type II Error

The exact critical values for a standard normal distribution, which the tests, * n CO , * n G , and n EP , set to approximate are presented in table 1 for different levels of significance while the corresponding empirical critical values for sample sizes n =20, 30, 50 and n = 100 are presented in table 2. It is well known that an appreciation of the critical value of a test beyond the expected (exact critical value) gives room for a wrong null hypothesis to be accepted, (type II error) while a depreciation of the critical value beyond the expected tends to allow rejection of a null hypothesis which is right, (type I error).

 

 

 

 

 

 

 

 

 

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