poissonp {VGAM} | R Documentation |
Estimating the density parameter of the distances from a fixed point to the u-th nearest point, in a plane or volume.
poissonp(ostatistic, dimension=2, link="loge", earg=list(), idensity=NULL, method.init=1)
ostatistic |
Order statistic. A single positive integer.
For example, the value 5 means the response are the distances of the
fifth nearest value to that point (usually over many planes or volumes).
|
dimension |
The value 2 or 3; 2 meaning a plane and 3 meaning a volume.
|
link |
Parameter link function applied to the (positive) density parameter,
called lambda below.
See Links for more choices.
|
earg |
List. Extra argument for the link.
See earg in Links for general information.
|
idensity |
Optional initial value for the parameter.
A NULL value means a value is obtained internally.
Use this argument if convergence failure occurs.
|
method.init |
An integer with value 1 or 2 which
specifies the initialization method for lambda.
If failure to converge occurs try another value
and/or else specify a value for idensity .
|
Suppose the number of points in any region of area A of the
plane is a Poisson random variable with mean lambda*A
(i.e., lambda is the density of the points).
Given a fixed point P, define D_1, D_2,... to be
the distance to the nearest point to P, second nearest to P,
etc. This VGAM family function estimates lambda
since the probability density function for D_u is easily derived,
u=1,2,.... Here, u corresponds to the
argument ostatistic
.
Similarly, suppose the number of points in any volume V is a
Poisson random variable with mean
lambda*V where, once again, lambda
is the density of the points.
This VGAM family function estimates lambda by
specifying the argument ostatistic
and using
dimension=3
.
The mean of D_u is returned as the fitted values. Newton-Raphson is the same as Fisher-scoring.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
rrvglm
and vgam
.
Convergence may be slow if the initial values are far from the solution. This often corresponds to the situation when the response values are all close to zero, i.e., there is a high density of points.
Formulae such as the means have not been fully checked.
T. W. Yee
y = rgamma(n <- 10, shape=exp(-1)) # Not good data! os = 2 fit = vglm(y ~ 1, poissonp(os, 2), tra=TRUE, cri="c") fit = vglm(y ~ 1, poissonp(os, 3), tra=TRUE, cri="c") # Slow convergence? fit = vglm(y ~ 1, poissonp(os, 3, idensi=1), tra=TRUE, cri="c") fitted(fit)[1:4] mean(y) coef(fit, matrix=TRUE) Coef(fit)