how to implement the one-sided tolerance limits using the noncentral t-student distribution in matlab

the two side one is already implemented in Matlab by nctcdf. I am interested to the one-side one because i need to find the characteristch value with a certain level of confidence. if this is expressed as k-times the st.dev from the mean, x=mean+k*st.dev, this means for instance to find k so that we are 75% confident that 95% of the population lies below x,

does anyone know how to do that?

Answer 1

[Davide Leonetti]

hi,

the tolerance limit for a normal distribution is , where and are the estimated mean and standard deviation, respectively.

Now, the value of can be estimated using the non central student t distribution. In particular, if you need to estimate the α tolerance limit for the p-percentile of your sample of N specimens:

where P=α

nu=N-1

delta=

being , the value of inverse standard normal distribution calculated in p