NON_CENTRAL_F_CDF Function (PV-WAVE Advantage)
Evaluates the noncentral F cumulative distribution function (CDF).
Usage
result = NON_CENTRAL_F_CDF (f, df_numerator, df_denominator, lambda)
Input Parameters
f—Scalar float value for which the noncentral F cumulative distribution function is to be evaluated. f must be non-negative.
df_numerator—Scalar float value indicating the numerator degrees of freedom of the noncentral F distribution. df_numerator must be positive.
df_denominator—Scalar float value indicating the denominator degrees of freedom of the noncentral F distribution. df_denominator must be positive.
lambda—Scalar float value indicating the noncentrality parameter. lambda must be non-negative.
Returned Value
result—The probability that a noncentral F random variable takes a value less than or equal to f.
Input Keywords
Inverse—If present and nonzero, evaluates the inverse of the noncentral F cumulative distribution function. If inverse is specified, then f represents the probability for which the inverse of the noncentral F function is to be evaluated. f must be non-negative and less than one.
Double—If present and nonzero, then double precision is used.
Discussion
If X is a noncentral chi-square random variable with noncentrality parameter λ and ν1 degrees of freedom, and Y is a chi-square random variable with ν2 degrees of freedom which is statistically independent of X, then:
F = (X/ν1)/(Y/ν2)
is a noncentral F-distributed random variable whose CDF is given by:
where the probability density function PDF(x) is given by:
and Γ(.) is the gamma function, ν1 = df_numerator, ν2 = df_denominator, λ = lambda, and f = f.
With a noncentrality parameter of zero, the noncentral F distribution is the same as the F distribution.
Example
This example traces out a portion of a noncentral F cumulative distribution function with parameters df_numerator = 100, df_denominator = 10, and lambda = 10.
PRO t_non_central_f_cdf
f = [0., .4, .8, 1.2, 1.6, 2.0, 2.8, 4.0]
df_numerator = 100.
df_denominator = 10.
lambda =10.
PRINT,"df_numerator:",$
STRING(df_numerator,Format="(f4.0)")
PRINT,"df_denominator:",$
STRING(df_denominator,Format="(f4.0)")
PRINT,"lambda:",$
STRING(lambda,Format="(f4.0)")
PRINT," f cdf(f)"
FOR i=0L, 7 DO BEGIN
cdfv = NON_CENTRAL_F_CDF( f(i),df_numerator, $
df_denominator, lambda)
PRINT,STRING(f(i),Format="(f5.1)")," ",$
STRING(cdfv,Format="(E12.4)")
ENDFOR
END
Output
df_numerator: 100
df_denominator: 10
lambda: 10
f cdf(f)
0.0 0.0000e+000
0.4 4.8879e-003
0.8 2.0263e-001
1.2 5.2114e-001
1.6 7.3385e-001
2.0 8.5041e-001
2.8 9.4713e-001
4.0 9.8536e-001
Version 2017.0
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