Normal Distribution - Parameter Estimation

Techniques

Cumulative Distribution Function

Cumulative Hazard Function

Weibull Distribution

Lognormal Distribution

Exponential Distribution

Exam

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The normal probability density function is

, -¥<x<¥ 

where m is the distribution mean, and
s is the distribution standard deviation.

If no censoring is involved, the distribution mean is estimated from the expression

where n is the sample size.

If no censoring is involved, the distribution standard deviation is estimated from the expression

However, when censored data are involved, parameter estimation becomes complicated. Three popular methods for parameter estimation for the normal distribution when censored data are encountered are

• maximum likelihood estimation,
• hazard plotting, and
• probability plotting.

After distribution parameters have been estimated, reliability estimations and predictions are used for evaluations.  The maximum likelihood estimation section explains how this can be done manually, but because of the complexity of the calculations, manual methods are not recommended.  The predicting module explains how to estimate reliability using The Reliability and Maintenance Analyst software package.