Noncentral t-distribution Calculator

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

Noncentral t-distribution
percentile x
degree of freedom ν
    1. ν>0
noncentrality λ
    1. λ≧0

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

    Noncentral t-distribution
    [1-7] /7Disp-Num
    [1]  2018/11/25 19:14   60 years old level or over / A teacher / A researcher / Not at All /
    Purpose of use
    Certified values for evaluating algorithms
    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.
    [2]  2017/05/11 18:04   60 years old level or over / Others / Useful /
    Purpose of use
    Wanted to use it as correct results to compare accuracy of other algorithms, but it appears to be unreliable.
    Incorrect result
    t = -65.85334569
    df = 9
    ncp = 31.6227766
    with 22 digits, reports pdf < 0
    [3]  2017/02/27 15:35   20 years old level / High-school/ University/ Grad student / Useful /
    Purpose of use
    To find critical T values and try and calculate power
    Please provide power for the input values.
    from Keisan
    You can use power by inputting ex) [3^2].
    [4]  2017/02/11 03:52   60 years old level or over / High-school/ University/ Grad student / Very /
    Purpose of use
    Compare with own method.
    [5]  2010/05/05 17:48   - / A researcher / Very /
    Purpose of use
    power analysis
    A wonderful public service. Thanks!
    [6]  2010/03/24 13:25   More than 60 / Self-employed people / Very /
    Purpose of use
    Work related calculation.
    [7]  2010/01/16 00:09   More than 60 / A researcher / Very /
    would like to be able to copy formula to a paper I am writing


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