Distribution Tests

Chi-Square Goodness of Fit Test#

Description#

Determines if the sample derives from a population with a normal distribution the mean and variance of which are calculated from the sample itself.

$H_{0}:$ Data in sample derives from a population with a normal distribution

$H_{1}:$ Data in sample does not derive from a population with a normal distribution

Returns#

• p-value
• decision
• Chi-Sq statistic

Jarque Bera Test#

Description#

Uses the sample skewness and sample kurtosis to determine if the sample derives from a normal distribution of unknown mean and variance.

$H_{0}:$ Data in sample derives from a population with a normal distribution

$H_{1}:$ Data in sample does not derive from a population with a normal distribution

Returns#

• p-value
• decision
• JB statistic

One Sample Kolmogorov Smirnov Test (KS1)#

Description#

Determines if the sample derives from a population with a standard normal distribution.

$H_{0}:$ Population CDF of the sample is the same as std normal CDF

Returns#

• p-value
• decision
• KS statistic

Two Sample Kolmogorov Smirnov Test (KS2)#

Description#

Determine if the two samples derive from the same distribution but make no assumptions about what that distribution is.

$H_{0}: \text{population CDF of the sample 1 is the same as population CDF of sample 2}$

Returns#

• p-value
• decision
• KS statistic