# PQStat - Baza Wiedzy

## Continuous probability distributions

• Normal distribution which is also called the Gaussian distribution or a bell curve, is one of the most important distribution in statistics. It has very interesting mathematical features and occurs very often in nature. It is usually designated with .

A density function is defined by:

where:

,

– an expected value of population (its measure is mean),

– standard deviation.

Normal distribution is a symmetrical distribution for a perpendicular line to axis of abscissae going through the points designating the mean, mode and median.

Normal distribution with a mean of and (), is so called a standardised normal distribution.

• t-Student distribution – the shape of t-Student distribution is similar to standardised normal distribution, but its tails are longer. The higher the number of degrees of freedom (), the more similar the shape of t-Student distribution to normal distribution.

A density function is defined by:

where:

,

– degrees of freedom (sample size is decreased by the number of limitations in given calculations),

is a Gamma function.

• Chi-square distribution, this is a right-skewed distribution with a shape depending on the number of degrees of freedom . The higher the number of degrees of freedom, the more similar the shape of distribution to the normal distribution.

Density function is defined by:

where:

,

– degrees of freedom (sample size is decreased by the number of limitations in given calculations),

is a Gamma function.

• Fisher-Snedecor distribution, this is a distribution which has a right tail that is longer and a shape that depends on the number of degrees of freedom and .

A density function is defined by:

where:

,

, – degrees of freedom (it is assumed that if i are independent with a distribution with adequately and degrees of freedom, than has a F Snedecor distribution ),

is a Beta function.