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Module stats

source code

Some of these functions, specifically f_value(), fprob(), betai(), and betacf(), are taken from stats.py "A collection of basic statistical functions for python." by Gary Strangman. They are copyright 1999-2007 Gary Strangman; All Rights Reserved and released under the MIT license.

The rest is copyright Greg Kochanski 2009.

Functions
float
 f_value(ER, EF, dfR, dfF) Returns an F-statistic given the following: source code

 fprob(dfnum, dfden, F) Returns the (1-tailed) significance level (p-value) of an F statistic given the degrees of freedom for the numerator (dfR-dfF) and the degrees of freedom for the denominator (dfF). source code

 betai(a, b, x) Returns the incomplete beta function: source code

 betacf(a, b, x) This function evaluates the continued fraction form of the incomplete Beta function, betai. source code

 gammaln(x) Returns the gamma function of xx. source code

 test_fprob(dfnum, dfden) source code

 t_value(ndof, p2sided=0.99) source code
float
 ltqnorm(p) Lower tail quantile for standard normal distribution function. source code
 Variables t_Table = `[(1, 0.5, 1.0), (1, 0.95, 12.71), (1, 0.98, 31.82), ...` __package__ = `'gmisclib'`

Imports: math

 Function Details

f_value(ER, EF, dfR, dfF)

source code

Returns an F-statistic given the following:

Parameters:
• `ER` - error associated with the null hypothesis (the Restricted model)
• `EF` - error associated with the alternate hypothesis (the Full model)
• `dfR` - degrees of freedom the Restricted model (null hypothesis)
• `dfF` - degrees of freedom associated with the Full model
Returns: float
f-statistic (not the probability)

fprob(dfnum, dfden, F)

source code

Returns the (1-tailed) significance level (p-value) of an F statistic given the degrees of freedom for the numerator (dfR-dfF) and the degrees of freedom for the denominator (dfF).

Usage: lfprob(dfnum, dfden, F) where usually dfnum=dfbn, dfden=dfwn

betai(a, b, x)

source code

Returns the incomplete beta function:

I-sub-x(a,b) = 1/B(a,b)*(Integral(0,x) of t^(a-1)(1-t)^(b-1) dt)

where a>=0,b>0 and B(a,b) = G(a)*G(b)/(G(a+b)) where G(a) is the gamma function of a. The continued fraction formulation is implemented here, using the betacf function. (Adapted from: Numerical Recipes in C.)

Usage: betai(a,b,x)

betacf(a, b, x)

source code

This function evaluates the continued fraction form of the incomplete Beta function, betai. (Adapted from: Numerical Recipes in C.)

Usage: betacf(a,b,x)

gammaln(x)

source code

Returns the gamma function of xx. Gamma(z) = Integral(0,infinity) of t^(z-1)exp(-t) dt. (Adapted from: Numerical Recipies in C. via code Copyright (c) 1999-2000 Gary Strangman and released under the LGPL.)

ltqnorm(p)

source code

Lower tail quantile for standard normal distribution function.

This function returns an approximation of the inverse cumulative standard normal distribution function. I.e., given P, it returns an approximation to the X satisfying P = Pr{Z <= X} where Z is a random variable from the standard normal distribution.

The algorithm uses a minimax approximation by rational functions and the result has a relative error whose absolute value is less than 1.15e-9.

Parameters:
• `p` (float (0,1))
Returns: float
Raises:
• `ValueError` - if the argument is out of range.

Author: Peter John Acklam

Notes:
• Time-stamp: 2000-07-19 18:26:14
• Downloaded from http://home.online.no/~pjacklam/notes/invnorm/impl/field/ltqnorm.txt GPK 4/22/2011. Documentation at http://home.online.no/~pjacklam/notes/invnorm/index.html, which is part of this package at .../references/stats_invnorm_pjacklam_2011.html.
• Modified from the author's original perl code (original comments follow below) by dfield@yahoo-inc.com. May 3, 2004.
Contacts:
pjacklam@online.no, Greg Kochanski <gpk@kochanski.org>

 ````[``(`1`, `0.5`, `1.0`)``,` `(`1`, `0.95`, `12.71`)``,` `(`1`, `0.98`, `31.82`)``,` `(`1`, `0.99`, `63.66`)``,` `(`1`, `0.995`, `127.3`)``,` `(`1`, `0.998`, `318.3`)``,` `(`1`, `0.999`, `636.6`)``,` `(`2`, `0.5`, `0.816`)``,` `...` ```