Difference between revisions of "BetaIaInv"

Latest revision as of 01:14, 16 January 2016

BetaIaInv(p, x, b)

Computes the inverse of the incomplete beta function, BetaI(p, a, b) with respect to «a». In other words, BetaIaInv returns a value such that BetaI(p, BetaIaInv(p, x, b), b) is equal to «x».

Note that this is similar to the BetaIInv(y, a, b) function, except that BetaIInv inverts BetaI with respect to the first parameter, «p», whereas BetaIaInv inverts it relative to the second parameter, «a».

The BetaIaInv function is closely related to the CumNegativeBinomInv function, which computes the inverse cumulative probability for a NegativeBinomial distribution. The two are related as:

CumNegativeBinomInv(u, r, p) + 1 = BetaIaInv(p, 1 - u, r)

Library

Advanced Math

History

The function was introduced in Analytica 4.5.

@@ Line 1: / Line 1: @@
 [[Category:Analytic Distribution Functions]]
-''(new to [[Analytica 4.5]])''
+== BetaIaInv(p, x, b) ==
+Computes the inverse of the incomplete beta function, [[BetaI]](p, a, b) with respect to «a».  In other words, [[BetaIaInv]] returns a value such that <code>BetaI(p, BetaIaInv(p, x, b), b)</code> is equal to «x».
-= BetaIaInv(p,x,b) =
+Note that this is similar to the [[BetaIInv]](y, a, b) function, except that [[BetaIInv]] inverts [[BetaI]] with respect to the first parameter, «p», whereas [[BetaIaInv]] inverts it relative to the second parameter, «a».
-Computes the inverse of the incomplete beta function, <code>[[BetaI]](p,a,b)</code> with respect to «a».  In other words, [[BetaIaInv]] returns a value such that <code>[[BetaI]](p,[[BetaIaInv]](p,x,b),b)</code> is equal to <code>x</code>.
+The [[BetaIaInv]] function is closely related to the [[CumNegativeBinomInv]] function, which computes the inverse cumulative probability for a [[NegativeBinomial]] distribution.  The two are related as:
-Note that this is similar to the <code>[[BetaIInv]](y,a,b)</code> function, except that [[BetaIInv]] inverts [[BetaI]] with respect to the first parameter, «p», whereas [[BetaIaInv]] inverts it relative to the second parameter, «a».
+:<code>CumNegativeBinomInv(u, r, p) + 1 = BetaIaInv(p, 1 - u, r)</code>
-The [[BetaIaInv]] function is closely related to the [[CumNegativeBinomialInv]] function, which computes the inverse cumulative probability for a [[NegativeBinomial]] distribution.  The two are related as:
+== Library ==
+Advanced Math
-:<code>CumNegativeBinomialInv(u,r,p)+1 = BetaIaInv(p,1-u,r)</code>
+==History==
+The function was introduced in [[Analytica 4.5]].
-= Library =
+== See Also ==
+* [[BetaI]]()
-Distribution Densities Library
+* [[BetaIInv]]()
+* [[CumNegativeBinomInv]]
-= See Also =
-* [[BetaI]](p,a,b)
-* [[BetaIInv]](y,a,b)
-* [[CumNegativeBinomialInv]]