DistFunc_kFactorPooled¶

DistFunc_kFactorPooled
(n, m, p, alpha)¶ Exact margin factor for bilateral covering interval of pooled Normal populations.
Parameters:  nint
The size of the population
 mint
The size of the pool
 pfloat
The probability level of the covering interval
 alphafloat
The confidence level of the covering interval
Returns:  kfloat
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 chisquare distribution with degrees of freedom and the solution of:
Examples
>>> import openturns as ot >>> k = ot.DistFunc.kFactorPooled(5, 3, 0.95, 0.9)