Estimates the parameters of a given distribution and evaluates the probability density function with these parameters. This can be useful for comparing histograms or kernel density estimates against a theoretical distribution.
stat_theodensity( mapping = NULL, data = NULL, geom = "line", position = "identity", ..., distri = "norm", n = 512, fix.arg = NULL, start.arg = NULL, na.rm = TRUE, show.legend = NA, inherit.aes = TRUE )
mapping  Set of aesthetic mappings created by 

data  The data to be displayed in this layer. There are three options: If A A 
geom  Use to override the default geom for 
position  Position adjustment, either as a string, or the result of a call to a position adjustment function. 
...  Other arguments passed on to 
distri  A 
n  An 
fix.arg  An optional named list giving values of fixed parameters of the named distribution. Parameters with fixed value are not estimated by maximum likelihood procedures. 
start.arg  A named list giving initial values of parameters for the named distribution. This argument may be omitted (default) for some distributions for which reasonable starting values are computed. 
na.rm  If 
show.legend  logical. Should this layer be included in the legends?

inherit.aes  If 
A Layer ggproto object.
Valid distri
arguments are the names of distributions for
which there exists a density function. The names should be given without a
prefix (typically 'd', 'r', 'q' and 'r'). For example: "norm"
for
the normal distribution and "nbinom"
for the negative binomial
distribution. Take a look at distributions
in the
stats package for an overview.
There are a couple of distribution for which there exist no reasonable
starting values, such as the Student tdistribution and the Fdistribution.
In these cases, it would probably be wise to provide reasonable starting
values as a named list to the start.arg
argument. When estimating a
binomial distribution, it would be best to supply the size
to the
fix.arg
argument.
By default, the y values are such that the integral of the distribution is
1, which scales well with the defaults of kernel density estimates. When
comparing distributions with absolute count histograms, a sensible choice
for aesthetic mapping would be aes(y = stat(count) * binwidth)
,
wherein binwidth
is matched with the bin width of the histogram.
For discrete distributions, the input data are expected to be integers, or doubles that can be divided by 1 without remainders.
Parameters are estimated using the
fitdist
()
function in the
fitdistrplus package using maximum likelihood estimation.
Hypergeometric and multinomial distributions from the stats package
are not supported.
probability density
density * number of observations  useful for comparing to histograms
density scaled to a maximum of 1
# A mixture of normal distributions where the standard deviation is # inverse gamma distributed resembles a cauchy distribution. x < rnorm(2000, 10, 1/rgamma(2000, 2, 0.5)) df < data.frame(x = x) ggplot(df, aes(x)) + geom_histogram(binwidth = 0.1, alpha = 0.3, position = "identity") + stat_theodensity(aes(y = stat(count) * 0.1, colour = "Normal"), distri = "norm", geom = "line") + stat_theodensity(aes(y = stat(count) * 0.1, colour = "Cauchy"), distri = "cauchy", geom = "line") + coord_cartesian(xlim = c(5, 15))# A negative binomial can be understood as a Poissongamma mixture df < data.frame(x = c(rpois(500, 25), rpois(500, rgamma(500, 5, 0.2))), cat = rep(c("Poisson", "Poissongamma"), each = 500)) ggplot(df, aes(x)) + geom_histogram(binwidth = 1, aes(fill = cat), alpha = 0.3, position = "identity") + stat_theodensity(aes(y = stat(count), colour = cat), distri = "nbinom", geom = "step", position = position_nudge(x = 0.5)) + stat_summary(aes(y = x, colour = cat, x = 1), fun.data = function(x){data.frame(xintercept = mean(x))}, geom = "vline")