EWGoF (version 2.2.2)

WNS.test: GoF tests based on the normalized spacings for the Weibull distribution

Description

Computes the Weibull GoF tests based on the normalized spacings: (TS) Tiku-Singh, (MSF) Mann-Scheuer-Fertig only with right censoring and (LOS) Lockhart-O'Reilly-Stephens test statistics.

Usage

WNS.test(x, type = "TS", s = 0, r = 0, nsim = 200)

Arguments

x

a numeric vector of data values.

type

the type of the test statistic used. "TS" is the default used test of Tiku-Singh,"MSF" for Mann-Scheuer-Fertig and "LOS" for Lockhart-O'Reilly-Stephens test statistic.

s

the index of the smallest observed value of x (s=0 if no left censoring).

r

the index of the largest observed value of x (r=0 if no right censoring).

nsim

an integer specifying the number of replicates used in Monte Carlo.

Value

An object of class htest.

Details

For these tests statistics, there is no need to estimate the unknown values of the Weibull parameters and they are among the most powerful ones especially TS and LOS.

The p-value computed is not the exact p-value: the null hypothesis distribution of some statistics is known only asymptotically and sometimes is not even known. The asymptotic approximation is not correct especially for small samples. That is why Monte Carlo simulation is needed to compute the p-value.

References

Tiku M.L. and Singh M., Testing the two-parameter Weibull distribution, Communications in Statistics, 10, 907-918, 1981.

Mann N.R., Scheuer E.M. and Fertig K.W., A new goodness-of-fit test for the two-parameter Weibull or extreme-value distribution, Communications in Statistics, 2, 383-400, 1973.

Lockhart R.A., O'Reilly F. and Stephens M.A., Tests for the extreme-value and Weibull distributions based on normalized spacings, Naval Research Logistics Quarterly, 33, 413-421, 1986.

Examples

# NOT RUN {
x1 <- rweibull(50,2,3)

#Apply the Tiku-Singh test with censored sample: 4 left censored and 5 right censored values
# }
# NOT RUN {
WNS.test(x1,type="TS",s=4,r=5)
# }
# NOT RUN {


# }