cdflib_wasm

cdflib_wasm is a WebAssembly packaging of the cdflib library as it appears in the presto project.

This library contains routines to compute cumulative distribution functions, inverses, and parameters of the distribution for the following set of statistical distributions:

(1) Beta
(2) Binomial
(3) Chi-square
(4) Noncentral Chi-square
(5) F
(6) Noncentral F
(7) Gamma
(8) Negative Binomial
(9) Normal
(10) Poisson
(11) Student's t
(12) Noncentral Student's t

Given values of all but one parameter of a distribution, the other is computed. These calculations are done with C pointers to Doubles.

http://www.netlib.org/random/ dcdflib.c README file

Install

npm install cdflib_wasm

Usage

For good practice, cdflib compiles asyncronously by default. You must therefore wait for the .compiled promise to be resolved.

const CdfLibWrapper = require("cdflib_wasm");
const cdflib = new CdfLibWrapper();
await cdflib.compiled;

It is possible to syncronously compile cdflib.

const cdflib = new CdfLibWrapper({ compileSync: true });
await cdflib.compiled;

Table of Content

| Functions | Documentation | | ------------------- | ------------------------------------------------------------------ | | cdfbet | Calculates parameters of the beta distribution. | | cdfbin | Calculates parameters of the binomial distribution. | | cdfchi | Calculates parameters of the chi-square distribution. | | cdfchn | Calculates parameters of the non-central chi-square distribution. | | cdff | Calculates parameters of the F distribution. | | cdffnc | Calculates parameters of the non-central F distribution. | | cdfgam | Calculates parameters of the gamma distribution. | | cdfnbn | Calculates parameters of the negative binomial distribution. | | cdfnor | Calculates parameters of the normal distribution. | | cdfpoi | Calculates parameters of the Poisson distribution. | | cdft | Calculates parameters of the student's t distribution. | | cdftnc | Calculates parameters of the non-central student's t distribution. |

Documentation

cdfbet

Calculates any one parameter of the beta distribution given values for the others.

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

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

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]

cdfbet_1(double x, double a, double b): double

cdfbet_1 Calculates P from X, A and B

const p = cdflib.cdfbet_1(x, a, b);

cdfbet_2(double p, double a, double b): double

cdfbet_2 Calculate X from P, A and B

const x = cdflib.cdfbet_2(p, a, b);

cdfbet_3(double p, double b, double x): double

cdfbet_3 Calculate A from P, X and B

const a = cdflib.cdfbet_3(p, b, x);

cdfbet_4(double a, double p, double x): double

cdfbet_4 Calculate B from P, X and A

const b = cdflib.cdfbet_4(a, p, x);

cdfbin

Calculates any one parameter of the binomial distribution given values for the others.

P <--> The cumulation from 0 to S of the binomial distribution.
    (Probablility of S or fewer successes in XN trials each
    with probability of success PR.)
    Input range: [0, 1].

S <--> The number of successes observed.
    Input range: [0, XN]
    Search range: [0, XN]

XN  <--> The number of binomial trials.
        Input range: (0, +infinity).
        Search range: [1E-100, 1E100]

PR  <--> The probability of success in each binomial trial.
        Input range: [0, 1].
        Search range: [0, 1]

cdfbin_1(double s, double xn, double pr): double

cdfbin_1 Calculate P from S, XN, PR

const p = cdflib.cdfbin_1(s, xn, pr);

cdfbin_2(double p, double xn, double pr): double

cdfbin_2 Calculate S from P, XN, PR

const s = cdflib.cdfbin_2(p, xn, pr);

cdfbin_3(double p, double s, double pr): double

cdfbin_3 Calculate XN from P, S, PR

const xn = cdflib.cdfbin_3(p, s, pr);

cdfbin_4(double p, double s, double xn): double

cdfbin_4 Calculate PR from P, S and XN

const pr = cdflib.cdfbin_4(p, s, xn);

cdfchi

Calculates any one parameter of the chi-squared distribution given values for the others.

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

X <--> Upper limit of integration of the non-central
    chi-square distribution.
    Input range: [0, +infinity).
    Search range: [0, 1E100]

DF <--> Degrees of freedom of the
        chi-square distribution.
        Input range: (0, +infinity).
        Search range: [ 1E-100, 1E100]

cdfchi_1(double x, double df): double

cdfchi_1 Calculate P from X and DF

const p = cdflib.cdfchi_1(x, df);

cdfchi_2(double p, double df): double

cdfchi_2 Calculate X from P and DF

const x = cdflib.cdfchi_2(p, df);

cdfchi_3(double p, double x): double

cdfchi_3 Calculate DF from P and X

const df = cdflib.cdfchi_3(p, x);

cdfchn

Calculates any one parameter of the non-central chi-squared distribution given values for the others.

P <--> The integral from 0 to X of the non-central chi-square
    distribution.
    Input range: [0, 1-1E-16).

X <--> Upper limit of integration of the non-central
    chi-square distribution.
    Input range: [0, +infinity).
    Search range: [0, 1E100]

DF <--> Degrees of freedom of the non-central
        chi-square distribution.
        Input range: (0, +infinity).
        Search range: [ 1E-100, 1E100]

NC <--> Non-centrality parameter of the non-central
        chi-square distribution.
        Input range: [0, +infinity).
        Search range: [0, 1E4]

Warning The computation time required for this routine is proportional to the noncentrality parameter (NC). Very large values of this parameter can consume immense computer resources. This is why the search range is bounded by 10,000.

cdfchn_1(double x, double df, double nc): double

cdfchn_1 Calculate P from X and DF

const p = cdflib.cdfchn_1(x, df, nc);

cdfchn_2(double p, double df, double nc): double

cdfchn_2 Calculate X from P, DF and NC

const x = cdflib.cdfchn_2(p, df, nc);

cdfchn_3(double x, double p, double nc): double

cdfchn_3 Calculate DF from P, X and NC

const df = cdflib.cdfchn_3(x, p, nc);

cdfchn_4(double x, double df, double p): double

cdfchn_4 Calculate NC from P, X and DF

const pnonc = cdflib.cdfchn_4(x, df, p);

cdff

Calculates any one parameter of the F distribution given values for the others.

P <--> The integral from 0 to F of the f-density.
        Input range: [0, 1].

F <--> Upper limit of integration of the f-density.
        Input range: [0, +infinity).
        Search range: [0, 1E100]

DFN < --> Degrees of freedom of the numerator sum of squares.
        Input range: (0, +infinity).
        Search range: [ 1E-100, 1E100]

DFD < --> Degrees of freedom of the denominator sum of squares.
        Input range: (0, +infinity).
        Search range: [ 1E-100, 1E100]

Warning The value of the cumulative F distribution is not necessarily monotone in either degrees of freedom. There thus may be two values that provide a given CDF value. This routine assumes monotonicity and will find an arbitrary one of the two values.

cdff_1(double dfn, double dfd, double f): double

cdff_1 Calculate P from F, DFN and DFD

const p = cdflib.cdff_1(dfc, dfd, f);

cdff_2(double dfn, double dfd, double p): double

cdff_2 Calculate F from P, DFN and DFD

const f = cdflib.cdff_2(dfn, dfd, p);

cdff_3(double p, double dfd, double f): double

cdff_3 Calculate DFN from P, F and DFD

const dfn = cdflib.cdff_3(p, dfd, f);

cdff_4(double dfn, double p, double f): double

cdff_4 Calculate DFD from P, F and DFN

const dfd = cdflib.cdff_4(dfn, p, f);

cdffnc

Calculates any one parameter of the Non-central F distribution given values for the others.

P <--> The integral from 0 to F of the non-central f-density.
        Input range: [0, 1-1E-16).

F <--> Upper limit of integration of the non-central f-density.
        Input range: [0, +infinity).
        Search range: [0, 1E100]

DFN < --> Degrees of freedom of the numerator sum of squares.
        Input range: (0, +infinity).
        Search range: [ 1E-100, 1E100]

DFD < --> Degrees of freedom of the denominator sum of squares.
        Must be in range: (0, +infinity).
        Input range: (0, +infinity).
        Search range: [ 1E-100, 1E100]

NC <-> The non-centrality parameter
        Input range: [0, infinity)
        Search range: [0, 1E4]

Warning

The computation time required for this routine is proportional to the noncentrality parameter (PNONC). Very large values of this parameter can consume immense computer resources. This is why the search range is bounded by 10,000.

Warning

The value of the cumulative noncentral F distribution is not necessarily monotone in either degrees of freedom. There thus may be two values that provide a given CDF value. This routine assumes monotonicity and will find an arbitrary one of the two values.

cdffnc_1(double dfn, double dfd, double nc, double f): double

cdffnc_1 Calculate P from F, DFN, DFD and NC

const p = cdflib.cdffnc_1(dfc, dfd, nc, f);

cdffnc_2(double dfn, double dfd, double nc, double p): double

cdffnc_2 Calculate F from P, DFN, DFD and NC

const f = cdflib.cdffnc_2(dfn, dfd, nc, p);

cdffnc_3(double p, double dfd, double nc, double f): double

cdffnc_3 Calculate DFN from P, F, DFD and NC

const dfn = cdflib.cdffnc_3(p, dfd, nc, f);

cdffnc_4(double dfn, double p, double nc, double f): double

cdffnc_4 Calculate DFD from P, F, DFN and NC

const dfd = cdflib.cdffnc_4(dfn, p, nc, f);

cdffnc_5(double dfn, double dfd, double p, double f): double

cdffnc_5 Calculate NC from P, F, DFN and DFD

const pnonc = cdflib.cdffnc_5(dfn, dfd, p, f);

cdfgam

Calculates any one parameter of the gamma distribution given values for the others.

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

X <--> The upper limit of integration of the gamma density.
    Input range: [0, +infinity).
    Search range: [0, 1E100]

SHAPE <--> The shape parameter of the gamma density.
        Input range: (0, +infinity).
        Search range: [1E-100, 1E100]

SCALE <--> The scale parameter of the gamma density.
        Input range: (0, +infinity).
        Search range: (1E-100, 1E100]

cdfgam_1(double scale, double shape, double x): double

cdfgam_1 Calculate P from X, SHAPE and SCALE

const p = cdflib.cdfgam_1(scale, shape, x);

cdfgam_2(double scale, double shape, double p): double

cdfgam_2 Calculate X from P, SHAPE and SCALE

const x = cdflib.cdfgam_2(scale, shape, p);

cdfgam_3(double scale, double p, double x): double

cdfgam_3 Calculate SHAPE from P, X and SCALE

const shape = cdflib.cdfgam_3(scale, p, x);

cdfgam_4(double p, double shape, double x): double

cdfgam_4 Calculate SCALE from P, X and SHAPE

const scale = cdflib.cdfgam_4(p, shape, x);

cdfnbn

Calculates any one parameter of the negative binomial distribution given values for the others.

The cumulative negative binomial distribution returns the probability that there will be F or fewer failures before the XNth success in binomial trials each of which has probability of success PR.

The individual term of the negative binomial is the probability of S failures before XN successes and is Choose(S, XN+S-1) * PR^(XN) * (1-PR)^S

P <--> The cumulation from 0 to S of the  negative
    binomial distribution.
    Input range: [0, 1].

S <--> The upper limit of cumulation of the binomial distribution.
    There are F or fewer failures before the XNth success.
    Input range: [0, +infinity).
    Search range: [0, 1E100]

XN  <--> The number of successes.
        Input range: [0, +infinity).
        Search range: [0, 1E100]

PR  <--> The probability of success in each binomial trial.
        Input range: [0, 1].
        Search range: [0, 1].

cdfnbn_1(double s, double xn, double pr): double

cdfnbn_1 Calculate P from S, XN, PR

const p = cdflib.cdfnbn_1(s, xn, pr);

cdfnbn_2(double p, double xn, double pr): double

cdfnbn_2 Calculate S from P, XN, PR

const s = cdflib.cdfnbn_2(p, xn, pr);

cdfnbn_3(double s, double p, double pr): double

cdfnbn_3 Calculate XN from P, S, PR

const xn = cdflib.cdfnbn_3(s, p, pr);

cdfnbn_4(double s, double p, double xn): double

cdfnbn_4 Calculate PR from P, S and XN

const pr = cdflib.cdfnbn_4(s, p, xn);

cdfnor

Calculates any one parameter of the normal distribution given values for the others.

P <--> The integral from -infinity to X of the normal density.
    Input range: (0, 1].

X < --> Upper limit of integration of the normal-density.
        Input range: ( -infinity, +infinity)

MEAN <--> The mean of the normal density.
        Input range: (-infinity, +infinity)

STD <--> Standard Deviation of the normal density.
        Input range: (0, +infinity).

Note The normal density is proportional to exp( - 0.5 * (( X - MEAN)/STD)**2)

cdfnor_1(double mean, double std, double x): double

cdfnor_1 Calculate P from X, MEAN and STD

const p = cdflib.cdfnor_1(mean, std, x);

cdfnor_2(double mean, double p, double std): double

cdfnor_2 Calculate X from P, MEAN and STD

const x = cdflib.cdfnor_2(mean, p, std);

cdfnor_3(double p, double std, double x): double

cdfnor_3 Calculate MEAN from P, X and STD

const mean = cdflib.cdfnor_3(p, std, x);

cdfnor_4(double mean, double p, double x): double

cdfnor_4 Calculate STD from P, X and MEAN

const sd = cdflib.cdfnor_4(mean, p, x);

cdfpoi

Calculates any one parameter of the Poisson distribution given values for the others.

P <--> The cumulation from 0 to S of the poisson density.
        Input range: [0, 1].

S <--> Upper limit of cumulation of the Poisson.
        Input range: [0, +infinity).
        Search range: [0, 1E100]

XLAM <--> Mean of the Poisson distribution.
        Input range: [0, +infinity).
        Search range: [0, 1E100]

cdfpoi_1(double s, double xlam): double

cdfpoi_1 Calculate P from S and XLAM

const p = cdflib.cdfpoi_1(s, xlam);

cdfpoi_2(double p, double xlam): double

cdfpoi_2 Calculate A from P and XLAM

const a = cdflib.cdfpoi_2(p, xlam);

cdfpoi_3(double p, double s): double

cdfpoi_3 Calculate XLAM from P and S

const xlam = cdflib.cdfpoi_3(p, s);

cdft

Calculates any one parameter of the student's t distribution given values for the others.

P <--> The integral from -infinity to t of the t-density.
        Input range: (0, 1].

T <--> Upper limit of integration of the t-density.
        Input range: ( -infinity, +infinity).
        Search range: [ -1E100, 1E100 ]

DF <--> Degrees of freedom of the t-distribution.
        Input range: (0 , +infinity).
        Search range: [1e-100, 1E10]

cdft_1(double df, double t): double

cdft_1 Calculate P from T and DF

const p = cdflib.cdft_1(df, t);

cdft_2(double df, double p): double

cdft_2 Calculate T from P and DF

const t = cdflib.cdft_2(p, df);

cdft_3(double p, double t): double

cdft_3 Calculate DF from P and T

const df = cdflib.cdft_3(p, t);

cdftnc

Calculates any one parameter of the non-central student's t distribution given values for the others.

P <--> The integral from -infinity to t of the noncentral t-den
    Input range: (0, 1].

T <--> Upper limit of integration of the noncentral t-density.
    Input range: ( -infinity, +infinity).
    Search range: [ -1E100, 1E100 ]

DF <--> Degrees of freedom of the noncentral t-distribution.
        Input range: (0 , +infinity).
        Search range: [1e-100, 1E10]

NC <--> Noncentrality parameter of the noncentral t-distribution.
            Input range: [-infinity , +infinity).
            Search range: [-1e4, 1E4]

cdftnc_1(double df, double nc, double t): double

cdftnc_1 Calculate P from T, DF, NC

const p = cdflib.cdftnc_1(df, nc, t);

cdftnc_2(double df, double nc, double p): double

cdftnc_2 Calculate T from P, DF, NC

const t = cdflib.cdftnc_2(df, nc, p);

cdftnc_3(double p, double nc, double t): double

cdftnc_3 Calculate DF from P, NC, T

const df = cdflib.cdftnc_3(p, nc, t);

cdftnc_4(double df, double p, double t): double

cdftnc_4 Calculate NC from P, DF, T

const pnonc = cdflib.cdftnc_4(df, p, t);

Credits

• presto for the cdflib C source
• node-cephes which I heavily borrow the wasm packaging from.