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)