stats_cdf_beta

(PECL stats >= 1.0.0)

stats_cdf_beta — CDF function for BETA Distribution. Calculates any one parameter of the beta distribution given values for the others.

说明

float stats_cdf_beta ( float $par1 , float $par2 , float $par3 , int $which )

Method Cumulative distribution function (P) is calculated directly by code associated with the following reference. DiDinato, A. R. and Morris, A. H. Algorithm 708: Significant Digit Computation of the Incomplete Beta Function Ratios. ACM Trans. Math. Softw. 18 (1993), 360-373. Computation of other parameters involve a search for a value that produces the desired value of P. The search relies on the monotonicity of P with the other parameter. Note The beta density is proportional to t^(A-1) * (1-t)^(B-1) Arguments P -- The integral from 0 to X of the chi-square distribution. Input range: [0, 1]. Q -- 1-P. Input range: [0, 1]. P + Q = 1.0. X -- Upper limit of integration of beta density. Input range: [0,1]. Search range: [0,1] Y -- 1-X. Input range: [0,1]. Search range: [0,1] X + Y = 1.0. A -- The first parameter of the beta density. Input range: (0, +infinity). Search range: [1D-100,1D100] B -- The second parameter of the beta density. Input range: (0, +infinity). Search range: [1D-100,1D100] STATUS -- 0 if calculation completed correctly -I if input parameter number I is out of range 1 if answer appears to be lower than lowest search bound 2 if answer appears to be higher than greatest search bound 3 if P + Q .ne. 1 4 if X + Y .ne. 1 BOUND -- Undefined if STATUS is 0 Bound exceeded by parameter number I if STATUS is negative. Lower search bound if STATUS is 1. Upper search bound if STATUS is 2.

参数

par1
par2
par3
which: Integer indicating which of the next four argument values is to be calculated from the others. Legal range: 1..4 which = 1 : Calculate P and Q from X,Y,A and B which = 2 : Calculate X and Y from P,Q,A and B which = 3 : Calculate A from P,Q,X,Y and B which = 4 : Calculate B from P,Q,X,Y and A

返回值

STATUS -- 0 if calculation completed correctly -I if input parameter number I is out of range 1 if answer appears to be lower than lowest search bound 2 if answer appears to be higher than greatest search bound 3 if P + Q .ne. 1 4 if X + Y .ne. 1

用户评论:

[#1] Anonymous [2009-12-30 00:29:40]

Additional Notes, taken from source.
WHICH --> Integer indicating which of the next four argument
values is to be calculated from the others.
Legal range: 1..4
iwhich = 1 : Calculate P and Q from X,Y,A and B
iwhich = 2 : Calculate X and Y from P,Q,A and B
iwhich = 3 : Calculate A from P,Q,X,Y and B
iwhich = 4 : Calculate B from P,Q,X,Y and A

P <--> The integral from 0 to X of the chi-square
distribution.
Input range: [0, 1].

Q <--> 1-P.
Input range: [0, 1].
P + Q = 1.0.

X <--> Upper limit of integration of beta density.
Input range: [0,1].
Search range: [0,1]

Y <--> 1-X.
Input range: [0,1].
Search range: [0,1]
X + Y = 1.0.

A <--> The first parameter of the beta density.
Input range: (0, +infinity).
Search range: [1D-100,1D100]

B <--> The second parameter of the beta density.
Input range: (0, +infinity).
Search range: [1D-100,1D100]