\deqn included in man pages fo distribution functions

man/dbs.Rd

@@ -60,14 +60,14 @@ qrbs( p, N, S, lower.tail = TRUE, log.p = FALSE )
   The Broken-stick distribution was proposed as a model for
   the expected abundance of elements in a collection:
 
-  n(i) = N/S (sum(from k=i to S) 1/k)
+  \deqn{n(i) = \frac{N}{S} \sum_{k=i}^S 1/k}{n(i) = N/S (sum(from k=i to S) 1/k)}
 
   where n(i) is the abundance in the i-th most abundant element
   (MacArthur 1960, May 1975).
   Hence the probability (or expected proportion of occurrences)
   in the i-th element is
 
-  p(i) = n(i)/N = n(i) = (sum(from k=i to S) 1/k) / S
+  \deqn{p(i) = \frac{n(i)}{S} = S^{-1}\sum_{k=i}^S 1/k}{p(i) = n(i)/N = (sum(from k=i to S) 1/k) / S}
 
   \code{[dpq]rbs} stands for "rank-abundance Broken-stick" and return
   probabilities and quantiles based on the expression above, for p(i).
@@ -78,7 +78,7 @@ qrbs( p, N, S, lower.tail = TRUE, log.p = FALSE )
   The probability density for a given abundance value in the Broken-stick model
   is given by 
 
-  p(x) = (1 - x/N)^(S-2) (S - 1)/N
+  \deqn{p(x) = \frac{S-1}{N} \left( 1 -  \frac{x}{N} \right)^{S-2}}{p(x) = (1 - x/N)^(S-2) (S - 1)/N}
 
   Where x is the abundance of a given element in the collection (May 1975).
   \code{[dpq]bs} return probabilities and quantiles according to the

man/dgs.Rd

@@ -52,12 +52,12 @@ qgs( p, k, S, lower.tail = TRUE, log.p = FALSE )
   proportion of occurrences) of the i-th most abundant element
   in a collection:
 
-  p(i) = C * k * (1-k)^(i-1)
+  \deqn{p(i) = C k (1-k)^{i-1}}{p(i) = C * k * (1-k)^(i-1)}
 
   where C is a normalization constant which makes the summation of p(i) over
   S equals to one:
 
-  C = 1/(1 - (1-k)^S)
+  \deqn{C = \frac{1}{1 - (1-k)^S}}{C = 1/(1 - (1-k)^S)}
 
   where S is the number of species in the sample.
 

man/dls.Rd

@@ -46,18 +46,18 @@ qls(p, N, alpha, lower.tail = TRUE, log.p = FALSE)
   was originally proposed by Fisher (1943) to relate the expected number
   of species in a sample from a biological community to the sample size as:
 
-  S = alpha * log(1 + N/alpha)
+%  \deqn{S = \alpha  \log \left( 1 + \frac{N}{\alpha} \right)}{S = alpha * log(1 + N/alpha)}
 
   Where alpha is the single parameter of the log-series distribution,
   often used as a diversity index. From this relation follows that the
   expected number of species with x individuals in the sample is
   
-  S(x) = alpha*X^x/x
+  \deqn{S(x) = \alpha \, \frac{X^x}{x}}{S(x) = alpha*X^x/x}
 
   Where X is a function of alpha and N, that tends to one as the sample
   size N increases:
 
-  X = N / (alpha+ N)
+  \deqn{X = \frac{N}{\alpha + N}}{X = N / (alpha+ N)}
   
   The density function used here is derived by Alonso et al. (2008,
   supplementary material). In ecology, this density distribution gives
@@ -67,7 +67,7 @@ qls(p, N, alpha, lower.tail = TRUE, log.p = FALSE)
   random variables that follow a log-series distribution. Thus, a random
   sample of a log-series is also a log-series distribution.
   
-  Hence, a log-series distribution is a model for species
+  Therefore, a log-series distribution is a model for species
   abundances distributions (SAD) under the assumptions that (a) species
   abundances in the community are independent identically distributed
   log-series variables, (b) sampling is a Poisson process, (c)
@@ -126,4 +126,4 @@ all.equal(pls(10,N=1000,alpha=50), sum(dls(1:10,N=1000,alpha=50))) # should be T
 
 ## qls is the inverse of pls
 all.equal(qls(CDF,N=100,alpha=5), x) # should be TRUE
-  }
+}

man/dman.Rd

@@ -50,7 +50,7 @@ qmand( p, N, s, v, lower.tail = TRUE, log.p = FALSE)
   of a given element from a set of \code{N} elements. This probability  is inversely proportional to a power \code{s} of the
   rank of the frequency of the element in the set. The density function is
 
-  p(x) = ((x+v)^(-s)) / sum(((1:N)+v)^(-s))
+  \deqn{p(x) = \frac{(x+v)^{-s}}{\sum_{i=1}^N (i+v)^{-s}}}{p(x) = ((x+v)^(-s)) / sum(((1:N)+v)^(-s))}
 
   Since p(x) is proportional to a power of \code{x}, the Zipf-Mandelbrodt distribution is a
   power distribution. The Zipf distribution is a special case when

man/dmzsm.Rd

@@ -59,12 +59,12 @@ pmzsm(q, J, theta, lower.tail=TRUE, log.p=FALSE)
   Alonso and McKane (2004) proposed an approximation for the density
   function for a large Poisson sample (J>100):
 
-  p(x) = N(x)/(sum(from 1 to S) N(x))
+  \deqn{p(x) = \frac{N(x)}{\sum_1^S N(x)}}{p(x) = N(x)/(sum(from 1 to S) N(x))}
 
   where S is the number of populations in the sample, and
   N(x) is the expected number of sampled populations of size x :
 
-  N(x) = theta/x (1 - x/J)^(theta -1)
+  \deqn{N(x) = \frac{\theta}{x (1 - x/J)^{\theta -1}}}{N(x) = theta/x (1 - x/J)^(theta -1)}
 
   Therefore, the mZSM 
   is a model for species

man/dpareto.Rd

@@ -54,15 +54,13 @@ values \code{NaN}, with a warning.
 
 \details{
 The Pareto distribution is a continuous power-law density distribution
-with \code{scale} and \code{shape} parameters with the form:
+with \code{scale} (a) and \code{shape} (b) parameters with the form:
 
-f(x) = shape * scale^shape / x^(shape+1)
+\deqn{f(x) = \frac{b a^b} {x^{b+1}}}{f(x) = shape * scale^shape / x^(shape+1)}
 
 For all x >= scale, and
 
-f(x) = 0
-
-otherwise.
+f(x) = 0 otherwise.
 
 The shape parameter is known as Pareto's index or tail index, and
 increases the decay of f(x). This distribution was originally used to

man/dpoilog.Rd

@@ -46,10 +46,12 @@ qpoilog( p, mu, sig, S = 30, lower.tail = TRUE, log.p = FALSE)
   where its single parameter lambda is a random variable with lognormal distribution. 
   The density function is 
 
-  p(x) = (exp(x*mu + x^2*sig/2)*(2*pi*sig)^(-1/2))/x! * g(y)
+  \deqn{p(x) = \frac{e^{x \mu + x^2 \sigma/2} (2 \pi \sigma)^{-1/2}}{x!}
+  \, g(y)}{p(x) = (exp(x*mu + x^2*sig/2)*(2*pi*sig)^(-1/2))/x! * g(y)}
 
-  where g(y) =
-  int_-infty^infty exp(-exp(y))*exp(((-y-mu-x*sig)^2)/(2*sig)) dy
+    where
+    \deqn{g(y) = \int_{-\infty}^\infty  \, e^{-e^y} \frac{e^{(-y-\mu-x
+	  \sigma)^2}}{2 \sigma}  \, dy}{g(y) = int_-infty^infty exp(-exp(y))*exp(((-y-mu-x*sig)^2)/(2*sig)) dy}
 
   (Bulmer 1974 eq.5). For x = 0, 1, 2, ... .
 

man/dpoix.Rd

@@ -33,8 +33,8 @@ dpoix(x, frac, rate, log=FALSE)
 \details{
   A compound Poisson-exponential distribution is a Poisson probability distribution
   where its single parameter lambda, is frac*n, at which n
-  is a random variable with exponential distribution. Thus, the expected value and variance are E[X] =
-  Var[X] = frac*n . The density function is
+  is a random variable with exponential distribution. Thus, the expected
+  value and variance are E[X] = Var[X] = frac*n . The density function is
 
   p(y) = rate*frac^y / (frac + rate)^(y+1)
 

man/dpower.Rd

@@ -46,10 +46,10 @@ qpower( p, s, lower.tail= TRUE, log.p=FALSE)
   The power density is a discrete probability distribution defined for
   integer x > 0:
 
-  p(x) = x^(-s) / zeta (s)
+  \deqn{p(x) = \frac{x^{-s}}{\zeta (s)}}{p(x) = x^(-s) / zeta (s)}
 
   Hence p(x) is proportional to a
-  negative power of 'x', given by the 's' exponent. The Riemann's zeta
+  negative power of 'x', given by the 's' exponent. The Riemann's \eqn{\zeta}{zeta}
   function is the integration constant.
 
   The power distribution can be used as a species abundance distribution (sad) model, which

man/dzipf.Rd

@@ -49,7 +49,7 @@ qzipf( p, N, s, lower.tail = TRUE, log.p = FALSE)
   law, this probability  is inversely proportional to a power \code{s} of the frequency
   rank of the element in the set. The density function is
 
-  p(x) = (x^(-s)) / sum((1:N)^(-s))
+  \deqn{p(x) = \frac{x^{-s}}{\sum_{i=1}^N i^{-s}}}{p(x) = ((x+v)^(-s)) / sum(((1:N)+v)^(-s))}
 
   Since p(x) is proportional to a power of \code{x}, the Zipf distribution is a
   power distribution. The Zeta distribution is a special case at the limit

man/trueLL.Rd

@@ -6,7 +6,7 @@
 \alias{trueLL,fitsad,ANY,missing,missing,numeric-method}
 \alias{trueLL,numeric,character,list,ANY,numeric-method}
 
-\title{True likelihood for continuous variables}}
+\title{True likelihood for continuous variables}
 
 \description{
   Calculates the correct likelihood for independent observations of a

vignettes/sads_intro.Rnw

@@ -17,7 +17,7 @@
 \newcommand{\R}{{\sf R}}
 \newcommand{\code}[1]{\texttt{#1}}
 \SweaveOpts{eval=TRUE, keep.source=TRUE, echo=TRUE}
-\VignetteIndexEntry{Introduction to sads}
+%\VignetteIndexEntry{Introduction to sads}
 
 \begin{document}