MQMF (version 0.1.1)

predfreq: predfreq is used for modal analysis of count data

Description

predfreq is used to calculate the expected frequencies (counts) from a series of Normal distributions that are combined to describe observed counts from a sample of the size distribution of a population, which may, or may not be made up of a number of cohorts. When used with a negative log-likelihood from a multinomial this can lead to estimates of the mean and standard deviation of the size of each cohort. Two approaches are possible. An approximate method that calculates the likelihood at the center of each size-class and a more precise analytical method that subtracts the cumulative probability of the bottom bound from each size- class from the upper bound. Usually the two are very close.

Usage

predfreq(pars, n, sizecl, midval = TRUE)

Arguments

pars

a vector of parameters, with the means first, followed by the standard deviations, followed by the proportion of total observations in each cohort expect the last, which is obtained through subtraction.

n

the sum of counts observed from nature

sizecl

a representation of the size-classes used, these can be the mid-points of each size-class or the lower and upper bounds of each class.

midval

if TRUE, the default, the approximate analytical approach will be used.

Value

a vector of expected frequencies

Examples

# NOT RUN {
mids <- seq(6,56,2) #size classes = 2 mm as in 5-7, 7-9,...
av <- c(18.0,34.5)   # the means
stdev <- c(2.75,5.5)  # the standard deviations
prop1 <- 0.55  # the proportion of observations in cohort 1
pars <-c(av,stdev,prop1)  # combine parameters into a vector
predf <- predfreq(pars,n=262,sizecl=mids,midval=TRUE)
oldpar <- par(no.readonly=TRUE)
plot1(mids,predf,xlab="Sizes",ylab="Predicted Frequency",lwd=2)
par(oldpar)
# }