# Noncentral t-distribution (percentile) Calculator

## Calculates the percentile from the lower or upper cumulative distribution function of the noncentral t-distribution.

 cumulative mode lower P upper Q cumulative distribution 0≦P,Q≦1 degree of freedom ν ν＞0 noncentrality λ λ≧0 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit
 $\normal Noncentral\ Student's\ t{\tiny-}distribution\\\hspace{240}t(x,\nu,\lambda)\\[10](1)\ probability\ density\\\ f(x,\nu,\lambda)={\small-}{\large\sum_{\small j=0}^{\small \infty}\frac{e^{-\frac{\lambda}{2}}(\frac{\lambda}{2})^j}{j!}\frac{(\frac{\nu}{\nu+x^2})^{\frac{\nu}{2}}(\frac{x^2}{\nu+x^2})^{\frac{1}{2}+j}}{B(\frac{\nu}{2},\frac{1}{2}+j)}\frac{2}{x}}\\\hspace{75}+{\large\sum_{\small j=\frac{1}{2}}^{\small \infty}\frac{e^{-\frac{\lambda}{2}}(\frac{\lambda}{2})^j}{j!}\frac{(\frac{\nu}{\nu+x^2})^{\frac{\nu}{2}}(\frac{x^2}{\nu+x^2})^{\frac{1}{2}+j}}{B(\frac{\nu}{2},\frac{1}{2}+j)}\frac{2}{x}}\\(2)\ lower\ cumulative\ distribution\\\hspace{25}P(x,\nu,\lambda)={\large\int_{\small-\infty}^{\hspace{25}\small x}}f(t,\nu,\lambda)dt\\(3)\ upper\ cumulative\ distribution\\\hspace{25}Q(x,\nu,\lambda)={\large\int_{\small x}^{\hspace{25pt}\small\infty}}f(t,\nu,\lambda)dt\\$
Noncentral t-distribution (percentile)
 [1-2] /2 Disp-Num5103050100200
[1]  2012/11/18 07:32   Male / 50 years old level / A teacher / A researcher / Very /
Purpose of use
Beautiful site! I would really love to get the code for the inverse nct calculation. Do you provide it?
from Keisan
Sorry, we don't provide the code for all calculations.
[2]  2011/09/09 03:09   Female / 20 years old level / An office worker / A public employee / Very /
Purpose of use
To calculate percentile for use in a client project on sampling data
Comment/Request
I want to replicate the formula used in your calculator in an excel sheet based model to produce a ready-to-go tool. Right now I am using both an excel sheet and your web link and for large quantities of data this to and fro procedure is tedious. If you could provide me with the calculations used behind the scene in your website I would be most grateful! Thank you,

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