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The RELIABILITY Procedure |
Note that you should not interpret the parameters and as representing the means and standard deviations for all of the distributions in Table 30.37. The normal is the only distribution in Table 30.37 for which this is the case.
Table 30.37: Distributions and Parameters for PROBPLOT and RELATIONPLOT StatementsParameters | |||||
Distribution | Density Function | Location | Scale | Shape | Threshold |
Normal | |||||
Lognormal | |||||
Lognormal | |||||
(base 10) | |||||
Extreme Value | |||||
Weibull | |||||
Exponential | |||||
Logistic | |||||
Log-logistic | |||||
The exponential distribution shown in Table 30.37 is a special case of the Weibull distribution with .The remaining distributions in Table 30.37 are related to one another as shown in Table 30.38. The threshold parameter, , is assumed to be 0 in Table 30.38.
Table 30.38: Relationship among Life DistributionsDistribution of T | Parameters | Distribution of Y=logT | Parameters | ||
Lognormal | Normal | ||||
Weibull | Extreme Value | ||||
Log-logistic | Logistic |
If a lifetime T has the generalized gamma distribution, then the logarithm of the lifetime X = log(T) has the generalized log-gamma distribution, with the following probability density function g(x). When the gamma distribution is specified, the logarithms of the lifetimes are used as responses, and the generalized log-gamma distribution is used to estimate the parameters by maximum likelihood.
When , the generalized log-gamma distribution reduces to the extreme value distribution with parameters and .In this case, the log lifetimes have the extreme value distribution, or, equivalently, the lifetimes have the Weibull distribution with parameters and .When ,the generalized log-gamma reduces to the normal distribution with parameters and . In this case, the (unlogged) lifetimes have the lognormal distribution with parameters and .This chapter uses the notation for the location, for the scale, and for the shape parameters for the generalized log-gamma distribution.
Distribution | Pr{Y=y} | Parameter | Parameter Name |
Binomial | p | binomial probability | |
Poisson | Poisson mean | ||
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