From 7d30ed65292439861d3f07f9ea274596624df7f2 Mon Sep 17 00:00:00 2001 From: Raymond Toy Date: Sun, 24 Jul 2022 15:24:17 -0700 Subject: [PATCH] Simplify the subsections in distrib Previously, the section for a random variable had a subsection for an introduction and one for the functions/variables. This change removes these subsections. Some random variables didn't have intros anyway. I think it looks better in the html docs to have the introductory stuff at the top of the page. Previously, you'd have to click around to get to the intro section. This matches more closely what the subsections in the Special Functions section does. --- doc/info/distrib.texi.m4 | 237 +---------------------------------------------- 1 file changed, 3 insertions(+), 234 deletions(-) diff --git a/doc/info/distrib.texi.m4 b/doc/info/distrib.texi.m4 index 6dbb7c8cd..037732367 100644 --- a/doc/info/distrib.texi.m4 +++ b/doc/info/distrib.texi.m4 @@ -352,20 +352,10 @@ Maxima knows the following kinds of continuous distributions. @node Normal Random Variable, Student's t Random Variable, Functions and Variables for continuous distributions, Functions and Variables for continuous distributions @subsection Normal Random Variable -@menu -* Introduction to Normal Random Variables:: -* Functions and Variables for Normal Random Variables:: -@end menu - -@node Introduction to Normal Random Variables, Functions and Variables for Normal Random Variables, Normal Random Variable, Normal Random Variable -@subsubsection Introduction to Normal Random Variables - Normal random variables (also called Gaussian) is denoted by m4_Normal_RV(m, s) where @math{m} is the mean and @math{s > 0} is the standard deviation. -@node Functions and Variables for Normal Random Variables, , Introduction to Normal Random Variables, Normal Random Variable -@subsubsection Functions and Variables for Normal Random Variables @anchor{pdf_normal} @deffn {Function} pdf_normal (@var{x},@var{m},@var{s}) Returns the value at @var{x} of the density function of a m4_Normal_RV(m,s) random variable, with @math{s>0}. To make use of this function, write first @code{load("distrib")}. @@ -585,13 +575,6 @@ To make use of this function, write first @code{load("distrib")}. @node Student's t Random Variable, Noncentral Student's t Random Variable, Normal Random Variable, Functions and Variables for continuous distributions @subsection Student's t Random Variable -@menu -* Introduction to Student's t Random Variable:: -* Functions and Variables for Student's t Random Variable:: -@end menu - -@node Introduction to Student's t Random Variable, Functions and Variables for Student's t Random Variable, Student's t Random Variable, Student's t Random Variable -@subsubsection Introduction to Student's t Random Variable Student's t random variable is denoted by m4_Student_T_RV(n) where @math{n} is the degrees of freedom with @math{n > 0}. If @math{Z} is @@ -605,8 +588,6 @@ m4_displaymath( has a Student's @math{t}-distribution with @math{n} degrees of freedom. -@node Functions and Variables for Student's t Random Variable, , Introduction to Student's t Random Variable, Student's t Random Variable -@subsubsection Functions and Variables for Student's t Random Variable @anchor{pdf_student_t} @deffn {Function} pdf_student_t (@var{x},@var{n}) Returns the value at @var{x} of the density function of a Student random variable m4_Student_T_RV(n), with @math{n>0} degrees of freedom. To make use of this function, write first @code{load("distrib")}. @@ -855,13 +836,6 @@ To make use of this function, write first @code{load("distrib")}. @node Noncentral Student's t Random Variable, Chi-squared Random Variable, Student's t Random Variable, Functions and Variables for continuous distributions @subsection Noncentral Student's t Random Variable -@menu -* Introduction to Noncentral Student's t Random Variable:: -* Functions and Variables for Noncentral Student's t Random Variable:: -@end menu - -@node Introduction to Noncentral Student's t Random Variable, Functions and Variables for Noncentral Student's t Random Variable, Noncentral Student's t Random Variable, Noncentral Student's t Random Variable -@subsubsection Introduction to Noncentral Student's t Random Variable Let @math{ncp} be the non-centrality parameter, @math{n} be the degrees of freedom for the non-central Student's @math{t} random variable. @@ -876,9 +850,6 @@ m4_displaymath( has a non-central Student's @math{t} distribution with non-centrality parameter @math{ncp}. -@node Functions and Variables for Noncentral Student's t Random Variable, , Introduction to Noncentral Student's t Random Variable, Noncentral Student's t Random Variable -@subsubsection Functions and Variables for Noncentral Student's t Random Variable - @anchor{pdf_noncentral_student_t} @deffn {Function} pdf_noncentral_student_t (@var{x},@var{n},@var{ncp}) Returns the value at @var{x} of the density function of a noncentral Student random variable m4_Noncentral_T_RV(n,ncp), with @math{n>0} degrees of freedom and noncentrality parameter @math{ncp}. To make use of this function, write first @code{load("distrib")}. @@ -1265,14 +1236,6 @@ To make use of this function, write first @code{load("distrib")}. @node Chi-squared Random Variable, Noncentral Chi-squared Random Variable, Noncentral Student's t Random Variable, Functions and Variables for continuous distributions @subsection Chi-squared Random Variable -@menu -* Introduction to Chi-squared Random Variable:: -* Functions and Variables for Chi-squared Random Variable:: -@end menu - -@node Introduction to Chi-squared Random Variable, Functions and Variables for Chi-squared Random Variable, Chi-squared Random Variable, Chi-squared Random Variable -@subsubsection Introduction to Chi-squared Random Variable - Let m4_math(<<>>, <<<@math{X_1, X_2, ..., X_k}>>>) be independent and identically distributed m4_Normal_RV(0,1) variables. Then m4_displaymath( @@ -1282,9 +1245,6 @@ m4_displaymath( is said to follow a chi-square distribution with @math{n} degrees of freedom. -@node Functions and Variables for Chi-squared Random Variable, , Introduction to Chi-squared Random Variable, Chi-squared Random Variable -@subsubsection Functions and Variables for Chi-squared Random Variable - @anchor{pdf_chi2} @deffn {Function} pdf_chi2 (@var{x},@var{n}) Returns the value at @var{x} of the density function of a Chi-square random variable m4_Chi2_RV(n), with @math{n>0}. @@ -1611,13 +1571,6 @@ To make use of this function, write first @code{load("distrib")}. @node Noncentral Chi-squared Random Variable, F Random Variable, Chi-squared Random Variable, Functions and Variables for continuous distributions @subsection Noncentral Chi-squared Random Variable -@menu -* Introduction to Noncentral Chi-squared Random Variable:: -* Functions and Variables for Noncentral Chi-squared Random Variable:: -@end menu - -@node Introduction to Noncentral Chi-squared Random Variable, Functions and Variables for Noncentral Chi-squared Random Variable, Noncentral Chi-squared Random Variable, Noncentral Chi-squared Random Variable -@subsubsection Introduction to Noncentral Chi-squared Random Variable Let m4_math(<<>>, <<<@math{X[1], X[2], ..., X[n]}>>>) be @math{n} independent normally distributed random variables with @@ -1635,9 +1588,6 @@ m4_displaymath( <<<\sum_{k=1}^n \mu_k^2>>>, <<<@math{sum(mu[k]^2, k, 1, n)}>>>) - -@node Functions and Variables for Noncentral Chi-squared Random Variable, , Introduction to Noncentral Chi-squared Random Variable, Noncentral Chi-squared Random Variable -@subsubsection Functions and Variables for Noncentral Chi-squared Random Variable @anchor{pdf_noncentral_chi2} @deffn {Function} pdf_noncentral_chi2 (@var{x},@var{n},@var{ncp}) Returns the value at @math{x} of the density function of a @@ -1838,13 +1788,7 @@ To make use of this function, write first @code{load("distrib")}. @node F Random Variable, Exponential Random Variable, Noncentral Chi-squared Random Variable, Functions and Variables for continuous distributions @subsection F Random Variable -@menu -* Introduction to F Random Variable:: -* Functions and Variables for F Random Variable:: -@end menu -@node Introduction to F Random Variable, Functions and Variables for F Random Variable, F Random Variable, F Random Variable -@subsubsection Introduction to F Random Variable Let @math{S_1} and @math{S_2} be independent random variables with a m4_math(\chi^2, chi-squared) distribution with degrees of freedom @math{n} and @math{m}, respectively. Then @@ -1853,8 +1797,6 @@ m4_displaymath( <<<@math{F = (S_1/n)/(S_2/m)}>>>) has an @math{F} distribution with @math{n} and @math{m} degrees of freedom. -@node Functions and Variables for F Random Variable, , Introduction to F Random Variable, F Random Variable -@subsubsection Functions and Variables for F Random Variable @anchor{pdf_f} @deffn {Function} pdf_f (@var{x},@var{m},@var{n}) Returns the value at @var{x} of the density function of a F random variable @math{F(m,n)}, with @math{m,n>0}. To make use of this function, write first @code{load("distrib")}. @@ -2113,19 +2055,11 @@ To make use of this function, write first @code{load("distrib")}. @node Exponential Random Variable, Lognormal Random Variable, F Random Variable, Functions and Variables for continuous distributions @subsection Exponential Random Variable -@menu -* Introduction to Exponential Random Variable:: -* Functions and Variables for Exponential Random Variable:: -@end menu -@node Introduction to Exponential Random Variable, Functions and Variables for Exponential Random Variable, Exponential Random Variable, Exponential Random Variable -@subsubsection Introduction to Exponential Random Variable The @emph{exponential distribution} is the probablity distribution of the time between events in a process where the events occur continuously and independently at a constant average rate. -@node Functions and Variables for Exponential Random Variable, , Introduction to Exponential Random Variable, Exponential Random Variable -@subsubsection Functions and Variables for Exponential Random Variable @anchor{pdf_exp} @deffn {Function} pdf_exp (@var{x},@var{m}) Returns the value at @var{x} of the density function of an m4_Exponential_RV(m) random variable, with @math{m>0}. @@ -2443,18 +2377,10 @@ To make use of this function, write first @code{load("distrib")}. @node Lognormal Random Variable, Gamma Random Variable, Exponential Random Variable, Functions and Variables for continuous distributions @subsection Lognormal Random Variable -@menu -* Introduction to Lognormal Random Variable:: -* Functions and Variables for Lognormal Random Variable:: -@end menu -@node Introduction to Lognormal Random Variable, Functions and Variables for Lognormal Random Variable, Lognormal Random Variable, Lognormal Random Variable -@subsubsection Introduction to Lognormal Random Variable The @emph{lognormal} distribution is distribution for a random variable whose logarithm is normally distributed. -@node Functions and Variables for Lognormal Random Variable, , Introduction to Lognormal Random Variable, Lognormal Random Variable -@subsubsection Functions and Variables for Lognormal Random Variable @anchor{pdf_lognormal} @deffn {Function} pdf_lognormal (@var{x},@var{m},@var{s}) Returns the value at @var{x} of the density function of a m4_Lognormal_RV(m,s) random variable, with @math{s>0}. To make use of this function, write first @code{load("distrib")}. @@ -2706,19 +2632,11 @@ To make use of this function, write first @code{load("distrib")}. @node Gamma Random Variable, Beta Random Variable, Lognormal Random Variable, Functions and Variables for continuous distributions @subsection Gamma Random Variable -@menu -* Introduction to Gamma Random Variable:: -* Functions and Variables for Gamma Random Variable:: -@end menu -@node Introduction to Gamma Random Variable, Functions and Variables for Gamma Random Variable, Gamma Random Variable, Gamma Random Variable -@subsubsection Introduction to Gamma Random Variable The @emph{gamma distribution} is a two-parameter family of probability distributions. Maxima uses the parameterization using the shape and scale for the first and second parameters of the distribution. -@node Functions and Variables for Gamma Random Variable, , Introduction to Gamma Random Variable, Gamma Random Variable -@subsubsection Functions and Variables for Gamma Random Variable @anchor{pdf_gamma} @deffn {Function} pdf_gamma (@var{x},@var{a},@var{b}) Returns the value at @var{x} of the density function of a m4_Gamma_RV(a,b) random variable, with @math{a,b>0}. To make use of this function, write first @code{load("distrib")}. @@ -2931,19 +2849,11 @@ To make use of this function, write first @code{load("distrib")}. @node Beta Random Variable, Continuous Uniform Random Variable, Gamma Random Variable, Functions and Variables for continuous distributions @subsection Beta Random Variable -@menu -* Introduction to Beta Random Variable:: -* Functions and Variables for Beta Random Variable:: -@end menu -@node Introduction to Beta Random Variable, Functions and Variables for Beta Random Variable, Beta Random Variable, Beta Random Variable -@subsubsection Introduction to Beta Random Variable The @emph{beta} distribution is a family of distributions defined over @math{[0,1]} parameterized by two positive shape parameters @math{a}, and @math{b}. -@node Functions and Variables for Beta Random Variable, , Introduction to Beta Random Variable, Beta Random Variable -@subsubsection Functions and Variables for Beta Random Variable @anchor{pdf_beta} @deffn {Function} pdf_beta (@var{x},@var{a},@var{b}) Returns the value at @var{x} of the density function of a m4_Beta_RV(a,b) random variable, with @math{a,b>0}. To make use of this function, write first @code{load("distrib")}. @@ -3166,17 +3076,10 @@ To make use of this function, write first @code{load("distrib")}. @node Continuous Uniform Random Variable, Logistic Random Variable, Beta Random Variable, Functions and Variables for continuous distributions @subsection Continuous Uniform Random Variable -@menu -* Introduction to Continuous Uniform Random Variable:: -* Functions and Variables for Continuous Uniform Random Variable:: -@end menu -@node Introduction to Continuous Uniform Random Variable, Functions and Variables for Continuous Uniform Random Variable, Continuous Uniform Random Variable, Continuous Uniform Random Variable -@subsubsection Introduction to Continuous Uniform Random Variable The @emph{continuous uniform} distribution is constant over the interval @math{[a,b]} and is zero elsewhere. -@node Functions and Variables for Continuous Uniform Random Variable, , Introduction to Continuous Uniform Random Variable, Continuous Uniform Random Variable -@subsubsection Functions and Variables for Continuous Uniform Random Variable + @anchor{pdf_continuous_uniform} @deffn {Function} pdf_continuous_uniform (@var{x},@var{a},@var{b}) Returns the value at @var{x} of the density function of a m4_Continuous_Uniform_RV(a,b) random variable, with @math{a0}. To make use of this function, write first @code{load("distrib")}. @@ -3577,15 +3472,7 @@ To make use of this function, write first @code{load("distrib")}. @node Pareto Random Variable, Weibull Random Variable, Logistic Random Variable, Functions and Variables for continuous distributions @subsection Pareto Random Variable -@menu -* Introduction to Pareto Random Variable:: -* Functions and Variables for Pareto Random Variable:: -@end menu -@node Introduction to Pareto Random Variable, , Pareto Random Variable, Pareto Random Variable -@subsubsection Introduction to Pareto Random Variable -@node Functions and Variables for Pareto Random Variable, , Introduction to Pareto Random Variable, Pareto Random Variable -@subsubsection Functions and Variables for Pareto Random Variable @anchor{pdf_pareto} @deffn {Function} pdf_pareto (@var{x},@var{a},@var{b}) Returns the value at @var{x} of the density function of a m4_Pareto_RV(a,b) random variable, with @math{a,b>0}. To make use of this function, write first @code{load("distrib")}. @@ -3779,15 +3666,7 @@ To make use of this function, write first @code{load("distrib")}. @node Weibull Random Variable, Rayleigh Random Variable, Pareto Random Variable, Functions and Variables for continuous distributions @subsection Weibull Random Variable -@menu -* Introduction to Weibull Random Variable:: -* Functions and Variables for Weibull Random Variable:: -@end menu -@node Introduction to Weibull Random Variable, , Weibull Random Variable, Weibull Random Variable -@subsubsection Introduction to Weibull Random Variable -@node Functions and Variables for Weibull Random Variable, , Introduction to Weibull Random Variable, Weibull Random Variable -@subsubsection Functions and Variables for Weibull Random Variable @anchor{pdf_weibull} @deffn {Function} pdf_weibull (@var{x},@var{a},@var{b}) Returns the value at @var{x} of the density function of a m4_Weibull_RV(a,b) random variable, with @math{a,b>0}. To make use of this function, write first @code{load("distrib")}. @@ -4016,18 +3895,10 @@ To make use of this function, write first @code{load("distrib")}. @node Rayleigh Random Variable, Laplace Random Variable, Weibull Random Variable, Functions and Variables for continuous distributions @subsection Rayleigh Random Variable -@menu -* Introduction to Rayleigh Random Variable:: -* Functions and Variables for Rayleigh Random Variable:: -@end menu -@node Introduction to Rayleigh Random Variable, Functions and Variables for Rayleigh Random Variable, Rayleigh Random Variable, Rayleigh Random Variable -@subsubsection Introduction to Rayleigh Random Variable The @emph{Rayleigh} distribution coincides with the m4_math(\chi^2, chi-squared) distribution with two degrees of freedom. -@node Functions and Variables for Rayleigh Random Variable, , Introduction to Rayleigh Random Variable, Rayleigh Random Variable -@subsubsection Functions and Variables for Rayleigh Random Variable @anchor{pdf_rayleigh} @deffn {Function} pdf_rayleigh (@var{x},@var{b}) Returns the value at @var{x} of the density function of a m4_Rayleigh_RV(b) random variable, with @math{b>0}. @@ -4378,20 +4249,12 @@ To make use of this function, write first @code{load("distrib")}. @node Laplace Random Variable, Cauchy Random Variable, Rayleigh Random Variable, Functions and Variables for continuous distributions @subsection Laplace Random Variable -@menu -* Introduction to Laplace Random Variable:: -* Functions and Variables for Laplace Random Variable:: -@end menu -@node Introduction to Laplace Random Variable, Functions and Variables for Laplace Random Variable, Laplace Random Variable, Laplace Random Variable -@subsubsection Introduction to Laplace Random Variable The @emph{Laplace} distribution is a continuous probability distribution that is sometimes called the double exponential distribution because it can be thought of as two exponential distributions spliced back to back. -@node Functions and Variables for Laplace Random Variable, , Introduction to Laplace Random Variable, Laplace Random Variable -@subsubsection Functions and Variables for Laplace Random Variable @anchor{pdf_laplace} @deffn {Function} pdf_laplace (@var{x},@var{a},@var{b}) Returns the value at @var{x} of the density function of a m4_Laplace_RV(a,b) random variable, with @math{b>0}. To make use of this function, write first @code{load("distrib")}. @@ -4579,13 +4442,7 @@ To make use of this function, write first @code{load("distrib")}. @node Cauchy Random Variable, Gumbel Random Variable, Laplace Random Variable, Functions and Variables for continuous distributions @subsection Cauchy Random Variable -@menu -* Introduction to Cauchy Random Variable:: -* Functions and Variables for Cauchy Random Variable:: -@end menu -@node Introduction to Cauchy Random Variable, Functions and Variables for Cauchy Random Variable, Cauchy Random Variable, Cauchy Random Variable -@subsubsection Introduction to Cauchy Random Variable The @emph{Cauchy} distribution (also known as the Lorentz distribution) is the distribution of of the ratio of two independent normally distributed random variables with mean zero. @@ -4594,8 +4451,6 @@ Note that the mean, variance, standard deviation, skewness coefficient, and kurtosis coefficient are all undefined for the Cauchy distribution. The integrals do not converge in this case. -@node Functions and Variables for Cauchy Random Variable, , Introduction to Cauchy Random Variable, Cauchy Random Variable -@subsubsection Functions and Variables for Cauchy Random Variable @anchor{pdf_cauchy} @deffn {Function} pdf_cauchy (@var{x},@var{a},@var{b}) Returns the value at @var{x} of the density function of a m4_Cauchy_RV(a,b) random variable, with @math{b>0}. To make use of this function, write first @code{load("distrib")}. @@ -4673,15 +4528,7 @@ To make use of this function, write first @code{load("distrib")}. @node Gumbel Random Variable, , Cauchy Random Variable, Functions and Variables for continuous distributions @subsection Gumbel Random Variable -@menu -* Introduction to Gumbel Random Variable:: -* Functions and Variables for Gumbel Random Variable:: -@end menu -@node Introduction to Gumbel Random Variable, , Gumbel Random Variable, Gumbel Random Variable -@subsubsection Introduction to Gumbel Random Variable -@node Functions and Variables for Gumbel Random Variable, , Introduction to Gumbel Random Variable, Gumbel Random Variable -@subsubsection Functions and Variables for Gumbel Random Variable @anchor{pdf_gumbel} @deffn {Function} pdf_gumbel (@var{x},@var{a},@var{b}) Returns the value at @var{x} of the density function of a m4_Gumbel_RV(a,b) random variable, with @math{b>0}. To make use of this function, write first @code{load("distrib")}. @@ -4920,7 +4767,7 @@ Maxima knows the following kinds of discrete distributions * Negative Binomial Random Variable:: @end menu -@node General Finite Discrete Random Variable, Poisson Random Variable, Functions and Variables for discrete distributions, Functions and Variables for discrete distributions +@node General Finite Discrete Random Variable, Binomial Random Variable, Functions and Variables for discrete distributions, Functions and Variables for discrete distributions @subsection General Finite Discrete Random Variable @anchor{pdf_general_finite_discrete} @@ -5114,13 +4961,6 @@ See @code{pdf_general_finite_discrete} for more details. @node Binomial Random Variable, Poisson Random Variable, General Finite Discrete Random Variable, Functions and Variables for discrete distributions @subsection Binomial Random Variable -@menu -* Introduction to Binomial Random Variable:: -* Functions for Binomial Random Variable:: -@end menu - -@node Introduction to Binomial Random Variable, Functions for Binomial Random Variable, General Finite Discrete Random Variable, General Finite Discrete Random Variable -@subsubsection Introduction to Binomial Random Variable The @emph{binomial distribution} with parameters @math{n} and @math{p} is a discrete probability distribution. It consists of @math{n} independent experiments where each experiment consists of a @@ -5132,9 +4972,6 @@ For example, a biased coin that comes up heads with probablity @math{k} heads in @math{n} tosses is given by the binomial distribution. -@node Functions for Binomial Random Variable, , Introduction to Binomial Random Variable, General Finite Discrete Random Variable -@subsubsection Functions for Binomial Random Variable - @anchor{pdf_binomial} @deffn {Function} pdf_binomial (@var{x},@var{n},@var{p}) Returns the value at @var{x} of the probability function of a m4_Binomial_RV(n,p) random variable, with @math{0 \leq p \leq 1} and @math{n} a positive integer. To make use of this function, write first @code{load("distrib")}. @@ -5340,26 +5177,15 @@ To make use of this function, write first @code{load("distrib")}. * Poisson Random Variable:: @end menu -@node Poisson Random Variable, Bernoulli Random Variable, General Finite Discrete Random Variable, Functions and Variables for discrete distributions +@node Poisson Random Variable, Bernoulli Random Variable, Binomial Random Variable, Functions and Variables for discrete distributions @subsection Poisson Random Variable -@menu -* Introduction to Poisson Random Variable:: -* Functions for Poisson Random Variable:: -@end menu - -@node Introduction to Poisson Random Variable, Functions for Poisson Random Variable, Poisson Random Variable, Poisson Random Variable -@subsubsection Introduction to Poisson Random Variable - The @emph{Poisson distribution} is a discrete probability distribution. It is the probability that a given number of events occur in a fixed interval when the events occur independently of the time of the last event, and the events occur with a known constant rate. -@node Functions for Poisson Random Variable, , Introduction to Poisson Random Variable, Poisson Random Variable -@subsubsection Functions for Poisson Random Variable - @anchor{pdf_poisson} @deffn {Function} pdf_poisson (@var{x},@var{m}) Returns the value at @var{x} of the probability function of a m4_Poisson_RV(m) random variable, with @math{m>0}. To make use of this function, write first @code{load("distrib")}. @@ -5561,23 +5387,12 @@ To make use of this function, write first @code{load("distrib")}. @node Bernoulli Random Variable, Geometric Random Variable, Poisson Random Variable, Functions and Variables for discrete distributions @subsection Bernoulli Random Variable -@menu -* Introduction to Bernoulli Random Variable:: -* Functions for Bernoulli Random Variable:: -@end menu - -@node Introduction to Bernoulli Random Variable, Functions for Bernoulli Random Variable, Bernoulli Random Variable, Bernoulli Random Variable -@subsubsection Introduction to Bernoulli Random Variable - The @emph{Bernoulli distribution} is a discrete probability distribution which takes on two values, 0 and 1. The value 1 occurs with probability @math{p}, and 0 occurs with probabilty @math{1-p}. It is equivalent to the m4_Binomial_RV(1,p) distribution (@pxref{Binomial Random Variable}) -@node Functions for Bernoulli Random Variable, , Introduction to Bernoulli Random Variable, Bernoulli Random Variable -@subsubsection Functions for Bernoulli Random Variable - @anchor{pdf_bernoulli} @deffn {Function} pdf_bernoulli (@var{x},@var{p}) Returns the value at @var{x} of the probability function of a m4_Bernoulli_RV(p) random variable, with @math{0 \leq p \leq 1}. @@ -5848,14 +5663,6 @@ See also @mrefdot{random} To make use of this function, write first @code{load(" @node Geometric Random Variable, Discrete Uniform Random Variable, Bernoulli Random Variable, Functions and Variables for discrete distributions @subsection Geometric Random Variable -@menu -* Introduction to Geometric Random Variable:: -* Functions for Geometric Random Variable:: -@end menu - -@node Introduction to Geometric Random Variable, Functions for Geometric Random Variable, Geometric Random Variable, Geometric Random Variable -@subsubsection Introduction to Geometric Random Variable - The @emph{Geometric distibution} is a discrete probability distribution. It is the distribution of the number Bernoulli trials that fail before the first success. @@ -5864,9 +5671,6 @@ Consider flipping a biased coin where heads occurs with probablity @math{p}. Then the probability of @math{k-1} tails in a row followed by heads is given by the m4_Geometric_RV(p) distribution. -@node Functions for Geometric Random Variable, , Introduction to Geometric Random Variable, Geometric Random Variable -@subsubsection Functions for Geometric Random Variable - @anchor{pdf_geometric} @deffn {Function} pdf_geometric (@var{x},@var{p}) Returns the value at @var{x} of the probability function of a m4_Geometric_RV(p) random variable, with @@ -6109,14 +5913,6 @@ This is interpreted as the probability of @math{x} failures before the first suc @node Discrete Uniform Random Variable, Hypergeometric Random Variable, Geometric Random Variable, Functions and Variables for discrete distributions @subsection Discrete Uniform Random Variable -@menu -* Introduction to Discrete Uniform Random Variable:: -* Functions for Discrete Uniform Random Variable:: -@end menu - -@node Introduction to Discrete Uniform Random Variable, Functions for Discrete Uniform Random Variable, Discrete Uniform Random Variable, Discrete Uniform Random Variable -@subsubsection Introduction to Discrete Uniform Random Variable - The @emph{Discrete uniform distribution} is a discrete probablity distribution where a finite number of values are equally likely to occur. The values are @math{1,2,3,...,n}. @@ -6124,9 +5920,6 @@ occur. The values are @math{1,2,3,...,n}. For example throwing a fair die of 6 sides numbered 1 through 6 follows a m4_DiscreteUniform_RV(1/6) distribution. -@node Functions for Discrete Uniform Random Variable, , Introduction to Discrete Uniform Random Variable, Discrete Uniform Random Variable -@subsubsection Functions for Discrete Uniform Random Variable - @anchor{pdf_discrete_uniform} @deffn {Function} pdf_discrete_uniform (@var{x},@var{n}) Returns the value at @var{x} of the probability function of a m4_DiscreteUniform_RV(n) random variable, with @math{n} a strictly positive integer. To make use of this function, write first @code{load("distrib")}. @@ -6319,14 +6112,6 @@ See also @mrefdot{random} To make use of this function, write first @code{load(" @node Hypergeometric Random Variable, Negative Binomial Random Variable, Discrete Uniform Random Variable, Functions and Variables for discrete distributions @subsection Hypergeometric Random Variable -@menu -* Introduction to Hypergeometric Random Variable:: -* Functions for Hypergeometric Random Variable:: -@end menu - -@node Introduction to Hypergeometric Random Variable, Functions for Hypergeometric Random Variable, Hypergeometric Random Variable, Hypergeometric Random Variable -@subsubsection Introduction to Hypergeometric Random Variable - The @emph{hypergeometric distribution} is a discrete probability distribution. @@ -6336,10 +6121,6 @@ We take out @math{n} objects, @emph{without} replacment. Then the hypergeometric distribution is the probability that exactly @math{k} objects are from class @math{A}. Of course @math{n \leq n_1 + n_2}. -@node Functions for Hypergeometric Random Variable, , Introduction to Hypergeometric Random Variable, Hypergeometric Random Variable -@subsubsection Functions for Hypergeometric Random Variable - - @anchor{pdf_hypergeometric} @deffn {Function} pdf_hypergeometric (@var{x},@var{n_1},@var{n_2},@var{n}) Returns the value at @var{x} of the probability function of a m4_Hypergeometric_RV(n1,n2,n) @@ -6587,14 +6368,6 @@ To make use of this function, write first @code{load("distrib")}. @node Negative Binomial Random Variable, , Hypergeometric Random Variable, Functions and Variables for discrete distributions @subsection Negative Binomial Random Variable -@menu -* Introduction to Negative Binomial Random Variable:: -* Functions for Negative Binomial Random Variable:: -@end menu - -@node Introduction to Negative Binomial Random Variable, Functions for Negative Binomial Random Variable, Negative Binomial Random Variable, Negative Binomial Random Variable -@subsubsection Introduction to Negative Binomial Random Variable - The @emph{negative binomial distribution} is a discrete probability distribution. Suppose we have a sequence of Bernoulli trials where each trial has two outcomes called ``success'' and ``failure'' where @@ -6603,10 +6376,6 @@ probability @math{1-p}. We observe the sequence until a predefined number @math{r} of sucesses have occurred. Then the number of failures seen will have a m4_NegativeBinomial_RV(r, p) distribution. -@node Functions for Negative Binomial Random Variable, , Introduction to Negative Binomial Random Variable, Negative Binomial Random Variable -@subsubsection Functions for Negative Binomial Random Variable - - @anchor{pdf_negative_binomial} @deffn {Function} pdf_negative_binomial (@var{x},@var{n},@var{p}) Returns the value at @var{x} of the probability function of a m4_NegativeBinomial_RV(n,p) random variable, with @math{0 < p \leq 1} and @math{n} a positive number. To make use of this function, write first @code{load("distrib")}. -- 2.11.4.GIT