Distribution Characteristics

The following information is an overview of various mathematical characteristics inherent in any probability distribution.

Probability Density Function

• Used for continuous random variables.

• NIST - probability density function

• StatSoft - probability density function

• Wikipedia - probability density function

• Arsham - probability density function

Sometimes referred to as the pdf

Often denoted as f(x)

Probability Mass Function

• Used for discrete random variables.

• NIST - probability mass function

• StatSoft - probability mass function (n/a)

• Wikipedia - probability mass function

• Arsham - probability mass function

Sometimes referred to as the pmf

Cumulative Distribution Function

• NIST - cumulative distribution function

• StatSoft - cumulative distribution function

• Wikipedia - cumulative distribution function

• Arsham - cumulative distribution function

Sometimes referred to as the cdf

Often denoted as F(x)

Quantile Function

• The inverse of the Cumulative Distribution Function.

• Also known as the Percent Point Function.

• NIST - quantile function

• StatSoft - quantile function

• Wikipedia - quantile function

• Arsham - quantile function

Survival Function

• NIST - survival function

• NIST - reliability or survival function

• StatSoft - survival function

• Wikipedia - survival function

• Arsham - survival function

Inverse Survival Function

• NIST - inverse survival function

• StatSoft - inverse survival function

• Wikipedia - inverse survival function

• Arsham - inverse survival function

Hazard Function

• NIST - hazard function

• NIST - failure or hazard rate

• StatSoft - hazard function

• Wikipedia - hazard function

• Arsham - hazard function

Cumulative Hazard Function

• NIST - cumulative hazard function

• StatSoft - cumulative hazard function

• Wikipedia - cumulative hazard function

• Arsham - cumulative hazard function

Moment Generating Function

• Used for continuous random variables.

• NIST

• StatSoft

• Wikipedia - mgf

• Arsham

Probability Generating Function

• Used for discrete random variables.

• NIST

• StatSoft

• Wikipedia - pgf

• Arsham

Characteristic Function

• NIST

• StatSoft

• Wikipedia - cf

• Arsham

Empirical Cumulative Distribution Function

• aka Empirical cdf (ecdf)

• NIST

• StatSoft

• Wikipedia - ecdf

• Arsham

Likelihood Function

• NIST

• StatSoft

• Wikipedia - likelihood

• Arsham