DADiSP Worksheet Functions > Function Categories > Special Functions > BETAINCINV
Calculates the inverse regularized incomplete beta function.
BETAINCINV(y, a, b, "tail")
y |
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A series or real number where |
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a |
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A series or real number |
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b |
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A series or real number |
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"tail" |
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Optional. A string, the upper or lower function flag.
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A scalar or series.
y = betainc(.3, .4, .5)
x = betaincinv(y, .4, .5)
x == 0.3.
W1: betainc({0.0, 0.5, 1.0}, 0.1, 0.2)
W2: betaincinv(W1)
W1 == {0.0, 0.5, 1.0}.
betaincinv(0..0.01..1, 8, 10);
xlabel("y");ylabel("I_x^{\;-1}(8,10)");label("Inverse Incomplete Beta Function")
returns a series consisting of the inverse regularized incomplete beta function for 101 values of y between 0 and 1, with a = 8 and b = 10.
The beta function is defined as:
The beta function is related to the gamma function by:
The incomplete beta function is a generalization of the beta function and defined as:
BETAINC computes the regularized incomplete beta function:
BETAINCINV computes the inverse of BETAINC.
"Tail" specifies the upper or lower inverse incomplete beta function where "lower" computes the inverse of the integral from 0 to x and "upper" computes the inverse of the integral from x to 1.
betaincinv(1 - y, a, b) = betaincinv(y, a, b, "upper")
If the inputs y, a and b are series, they must all be of the same size.