From: Mario R. R. <rio...@us...> - 2009-05-30 12:49:13
|
Update of /cvsroot/maxima/maxima/doc/info In directory 23jxhf1.ch3.sourceforge.com:/tmp/cvs-serv25874/doc/info Modified Files: distrib.texi Log Message: Make use of incomplete beta and inverse erf. Index: distrib.texi =================================================================== RCS file: /cvsroot/maxima/maxima/doc/info/distrib.texi,v retrieving revision 1.13 retrieving revision 1.14 diff -u -d -r1.13 -r1.14 --- distrib.texi 28 Dec 2008 17:37:35 -0000 1.13 +++ distrib.texi 30 May 2009 12:49:09 -0000 1.14 @@ -292,6 +292,21 @@ @deffn {Function} quantile_normal (@var{q},@var{m},@var{s}) Returns the @var{q}-quantile of a @math{Normal(m,s)} random variable, with @math{s>0}; in other words, this is the inverse of @code{cdf_normal}. Argument @var{q} must be an element of @math{[0,1]}. To make use of this function, write first @code{load(distrib)}. +@c ===beg=== +@c load (distrib)$ +@c quantile_normal(95/100,0,1); +@c float(%); +@c ===end=== +@example +(%i1) load (distrib)$ +(%i2) quantile_normal(95/100,0,1); + 9 +(%o2) sqrt(2) inverse_erf(--) + 10 +(%i3) float(%); +(%o3) 1.644853626951472 +@end example + @opencatbox @category{Package distrib} @closecatbox @@ -374,21 +389,23 @@ @deffn {Function} cdf_student_t (@var{x},@var{n}) -Returns the value at @var{x} of the distribution function of a Student random variable @math{t(n)}, with @math{n>0} degrees of freedom. This function has no closed form and it is numerically computed if the global variable @code{numer} equals @code{true}, otherwise it returns a nominal expression. +Returns the value at @var{x} of the distribution function of a Student random variable @math{t(n)}, with @math{n>0} degrees of freedom. @c ===beg=== @c load (distrib)$ @c cdf_student_t(1/2, 7/3); -@c %,numer; +@c float(%); @c ===end=== @example (%i1) load (distrib)$ (%i2) cdf_student_t(1/2, 7/3); - 1 7 -(%o2) cdf_student_t(-, -) - 2 3 -(%i3) %,numer; -(%o3) .6698450596140417 + 7 1 28 + beta_incomplete_regularized(-, -, --) + 6 2 31 +(%o2) 1 - ------------------------------------- + 2 +(%i3) float(%); +(%o3) .6698450596140415 @end example @opencatbox @@ -1005,21 +1022,21 @@ @deffn {Function} cdf_f (@var{x},@var{m},@var{n}) -Returns the value at @var{x} of the distribution function of a F random variable @math{F(m,n)}, with @math{m,n>0}. This function has no closed form and it is numerically computed if the global variable @code{numer} equals @code{true}, otherwise it returns a nominal expression. +Returns the value at @var{x} of the distribution function of a F random variable @math{F(m,n)}, with @math{m,n>0}. @c ===beg=== @c load (distrib)$ @c cdf_f(2,3,9/4); -@c %,numer; +@c float(%); @c ===end=== @example (%i1) load (distrib)$ (%i2) cdf_f(2,3,9/4); - 9 -(%o2) cdf_f(2, 3, -) - 4 -(%i3) %,numer; -(%o3) 0.66756728179008 + 9 3 3 +(%o2) 1 - beta_incomplete_regularized(-, -, --) + 8 2 11 +(%i3) float(%); +(%o3) 0.66756728179008 @end example @opencatbox @@ -1411,6 +1428,20 @@ @deffn {Function} quantile_lognormal (@var{q},@var{m},@var{s}) Returns the @var{q}-quantile of a @math{Lognormal(m,s)} random variable, with @math{s>0}; in other words, this is the inverse of @code{cdf_lognormal}. Argument @var{q} must be an element of @math{[0,1]}. To make use of this function, write first @code{load(distrib)}. +@c ===beg=== +@c load (distrib)$ +@c quantile_lognormal(95/100,0,1); +@c float(%); +@c ===end=== +@example +(%i1) load (distrib)$ +(%i2) quantile_lognormal(95/100,0,1); + sqrt(2) inverse_erf(9/10) +(%o2) %e +(%i3) float(%); +(%o3) 5.180251602233015 +@end example + @opencatbox @category{Package distrib} @closecatbox @@ -1607,23 +1638,21 @@ @deffn {Function} cdf_beta (@var{x},@var{a},@var{b}) -Returns the value at @var{x} of the distribution function of a @math{Beta(a,b)} random variable, with @math{a,b>0}. - -This function has no closed form and it is numerically computed if the global variable @code{numer} equals @code{true}, otherwise it returns a nominal expression. +Returns the value at @var{x} of the distribution function of a @math{Beta(a,b)} random variable, with @math{a,b>0}. @c ===beg=== @c load (distrib)$ @c cdf_beta(1/3,15,2); -@c %,numer; +@c float(%); @c ===end=== @example (%i1) load (distrib)$ (%i2) cdf_beta(1/3,15,2); - 1 -(%o2) cdf_beta(-, 15, 2) - 3 -(%i3) %,numer; -(%o3) 7.666089131388224E-7 + 11 +(%o2) -------- + 14348907 +(%i3) float(%); +(%o3) 7.666089131388195E-7 @end example @opencatbox @@ -2631,21 +2660,19 @@ @deffn {Function} cdf_binomial (@var{x},@var{n},@var{p}) Returns the value at @var{x} of the distribution function of a @math{Binomial(n,p)} random variable, with @math{0<p<1} and @math{n} a positive integer. -This function is numerically computed if the global variable @code{numer} equals @code{true}, otherwise it returns a nominal expression. - @c ===beg=== @c load (distrib)$ @c cdf_binomial(5,7,1/6); -@c cdf_binomial(5,7,1/6), numer; +@c float(%); @c ===end=== @example (%i1) load (distrib)$ (%i2) cdf_binomial(5,7,1/6); - 1 -(%o2) cdf_binomial(5, 7, -) - 6 -(%i3) cdf_binomial(5,7,1/6), numer; -(%o3) .9998713991769548 + 7775 +(%o2) ---- + 7776 +(%i3) float(%); +(%o3) .9998713991769548 @end example @opencatbox @@ -3325,21 +3352,19 @@ @deffn {Function} cdf_negative_binomial (@var{x},@var{n},@var{p}) Returns the value at @var{x} of the distribution function of a @math{Negative Binomial(n,p)} random variable, with @math{0<p<1} and @math{n} a positive integer. -This function is numerically computed if the global variable @code{numer} equals @code{true}, otherwise it returns a nominal expression. - @c ===beg=== @c load (distrib)$ @c cdf_negative_binomial(3,4,1/8); -@c cdf_negative_binomial(3,4,1/8), numer; +@c float(%); @c ===end=== @example (%i1) load (distrib)$ (%i2) cdf_negative_binomial(3,4,1/8); - 1 -(%o2) cdf_negative_binomial(3, 4, -) - 8 -(%i3) cdf_negative_binomial(3,4,1/8), numer; -(%o3) .006238937377929698 + 3271 +(%o2) ------ + 524288 +(%i3) float(%); +(%o3) .006238937377929687 @end example @opencatbox |