What is a parameter?

Parameters are descriptive measures of an entire population that may be used as the inputs for a probability distribution function (PDF) to generate distribution curves. Parameters are usually signified by Greek letters to distinguish them from sample statistics. For example, the population mean is represented by the Greek letter mu (μ) and the population standard deviation by the Greek letter sigma (σ). Parameters are fixed constants, that is, they do not vary like variables. However, their values are usually unknown because it is infeasible to measure an entire population.

Each distribution is entirely defined by several specific parameters, usually between one and three. The following table provides examples of the parameters required for three distributions. The parameter values determine the location and shape of the curve on the plot of distribution, and each unique combination of parameter values produces a unique distribution curve.
Distribution Parameter 1 Parameter 2 Parameter 3
Chi-square Degrees of freedom    
Normal Mean Standard deviation  
3-Parameter Gamma Shape Scale Threshold
For example, a normal distribution is defined by two parameters, the mean and standard deviation. If these are specified, the entire distribution is precisely known.

The solid line represents a normal distribution with a mean of 100 and a standard deviation of 15. The dashed line is also a normal distribution, but it has a mean of 120 and a standard deviation of 30.

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