Question

Twenty-five measurements of the time a client waits for a server is recorded in seconds. Which probability density model - normal, log normal, or Weibull - appears to provide the most suitable fit to the data?

1.21	4.19	1.95	6.88	3.97
9.09	6.91	1.90	10.60	0.51
2.23	13.99	8.22	8.08	4.70
4.67	0.50	0.92	4.15	7.24
4.86	1.89	6.44	0.15	17.34

Identify the associated parameter estimates. Use these parameter estimates to determine the mean and variance.

Answer 1

We will conduct Goodness of Fit Test for various distributions and check and compare p value.

Taking alpha = .05 (level of significance)

Distribution	AD	P
Normal	0.650	0.080
Lognormal	0.743	0.046
Weibull	0.271	>0.250

For lognormal since pvalue = 0.046 which is less than0.05, thus data suggest that it does not follows lognormal distribution.

In case of normal & weibull both have p values > 0.05 and follows their respective distribution significantly. But since p value for weibull is > p value for normal distribution. Thus data shows that it follows weibull distribution more significantly than normal.

b.

ML Estimates of Distribution Parameters

Distribution	Location	Shape	Scale	Threshold
Weibull		1.18814	5.60911