hazrate.like  R Documentation 
Computes the hazard rate likelihood of offtransect distances, given parameters. Primarily used as a minimization objective during distance function estimation.
hazrate.like(
a,
dist,
covars = NULL,
w.lo = units::set_units(0, "m"),
w.hi = max(dist),
series = "cosine",
expansions = 0,
scale = TRUE,
pointSurvey = FALSE
)
a 
A vector of likelihood parameter values. Length and meaning
depend on 
dist 
A numeric vector containing the observed distances. 
covars 
Data frame containing values of covariates at
each observation in 
w.lo 
Scalar value of the lowest observable distance.
This is the left truncation of sighting distances in

w.hi 
Scalar value of the largest observable distance.
This is the right truncation of sighting distances in

series 
A string specifying the type of expansion to use.
Currently, valid values are 'simple', 'hermite', and 'cosine'; but, see

expansions 
A scalar specifying the number of terms in

scale 
Logical scalar indicating whether or not to scale
the likelihood so it integrates to 1. This parameter is used to
stop recursion in other functions.
If 
pointSurvey 
Boolean. TRUE if 
The hazard rate likelihood is
f(x\sigma,k) = 1  \exp((x/\sigma)^{k})
where \sigma
determines location
(i.e., distance at which the function equals 1  exp(1) = 0.632),
and k
determines slope of the function
at \sigma
(i.e., larger k equals steeper
slope at \sigma
). For distance analysis,
the valid range for both \sigma
and k is
\geq 0
.
Expansion Terms: If expansions
= e
(e > 0), the expansion function specified by
series
is called (see for example
cosine.expansion
). Assuming
h_{ij}(x)
is the j^{th}
expansion term for the i^{th}
distance and that
c_1, c_2, \dots, c_k
are
(estimated) coefficients for the expansion terms, the
likelihood contribution for the i^{th}
distance is,
f(xa,b,c_1,c_2,\dots,c_e) = f(xa,b)(1 +
\sum_{j=1}^{e} c_j h_{ij}(x)).
A numeric vector the same length and order as
dist
containing the likelihood contribution for
corresponding distances in dist
.
Assuming L
is the returned vector from one of these
functions, the full log likelihood of all the data is
sum(log(L), na.rm=T)
. Note that the
returned likelihood value for distances less than
w.lo
or greater than w.hi
is NA
,
and thus it is prudent to use na.rm=TRUE
in the
sum. If scale
= TRUE, the integral of the likelihood
from w.lo
to w.hi
is 1.0. If scale
=
FALSE, the integral of the likelihood is
arbitrary.
dfuncEstim
,
halfnorm.like
,
uniform.like
,
negexp.like
,
Gamma.like
## Not run:
x < seq(0, 100, length=100)
# Plots showing effects of changes in sigma
plot(x, hazrate.like(c(20, 5), x), type="l", col="red")
plot(x, hazrate.like(c(40, 5), x), type="l", col="blue")
# Plots showing effects of changes in beta
plot(x, hazrate.like(c(50, 20), x), type="l", col="red")
plot(x, hazrate.like(c(50, 2), x), type="l", col="blue")
## End(Not run)
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