# Noncentral t-distribution Calculator

## Calculates the probability density function and lower and upper cumulative distribution functions of the noncentral t-distribution. | ||

・when λ=0, this comes to the student's t-distribution. |

Noncentral t-distribution

[1-7] /7 | Disp-Num |

- Purpose of use
- Certified values for evaluating algorithms
- Comment/Request
- It would be very useful if reliable; but not very, since it is currently unable to recognize when it is in trouble.

A year and a half ago, another user reported an example where the reported pdf was negative, which is of course impossible. Not only has that not been fixed in the last year and a half, the reported cdf from that example is easily recognized as ridiculous. It is well know that when t<0 and ncp>0, then F(t,df,ncp) < P(-ncp), where F is the noncentral t cdf, and P is the standard normal cdf. For that posted example (t=-65.85334569, df=9, ncp=31.6227766), that means that F(t,df,ncp) < 9e-220, yet you report it to be 0.0044...

Your calculator does work with t*ncp<0 (e.g. t=-1, df=1, ncp=1), but without more information it is difficult to know when it can be trusted.

[1] 2018/11/25 19:14 60 years old level or over / A teacher / A researcher / Not at All /

- Purpose of use
- Wanted to use it as correct results to compare accuracy of other algorithms, but it appears to be unreliable.
- Comment/Request
- Incorrect result

t = -65.85334569

df = 9

ncp = 31.6227766

with 22 digits, reports pdf < 0

[2] 2017/05/11 18:04 60 years old level or over / Others / Useful /

- Purpose of use
- To find critical T values and try and calculate power
- Comment/Request
- Please provide power for the input values.
- from Keisan
- You can use power by inputting ex) [3^2].

[3] 2017/02/27 15:35 20 years old level / High-school/ University/ Grad student / Useful /

- Purpose of use
- Compare with own method.

[4] 2017/02/11 03:52 60 years old level or over / High-school/ University/ Grad student / Very /

- Purpose of use
- power analysis
- Comment/Request
- A wonderful public service. Thanks!

[5] 2010/05/05 17:48 - / A researcher / Very /

- Purpose of use
- Work related calculation.
- Comment/Request
- Thanks

[6] 2010/03/24 13:25 More than 60 / Self-employed people / Very /

- Comment/Request
- would like to be able to copy formula to a paper I am writing

[7] 2010/01/16 00:09 More than 60 / A researcher / Very /

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