# DistFunc_kFactorPooled¶

DistFunc_kFactorPooled(n, m, p, alpha)

Exact margin factor for bilateral covering interval of pooled Normal populations.

Parameters: n : int The size of the population m : int The size of the pool p : float The probability level of the covering interval alpha : float The confidence level of the covering interval k : float The margin factor

Notes

This method allows to compute the exact margin factor of a pool of Normal populations of size with unknown means and unknown common variance . Let be the empirical mean of the ith population and the empirical pooled variance. The covering factor is such that the intervals satisfy:

for . It reduces to find such that:

where is the density function of the normal distribution with a mean equals to 0 and a variance equals to , and the function defined by:

where is the complementary distribution function of a chi-square distribution with degrees of freedom and the solution of:

Examples

>>> import openturns as ot
>>> k = ot.DistFunc.kFactorPooled(5, 3, 0.95, 0.9)