mlbinom {univariateML} | R Documentation |
Binomial distribution maximum likelihood estimation
Description
For the density function of the Binomial distribution see Binomial.
Usage
mlbinom(x, na.rm = FALSE, ...)
Arguments
x |
a (non-empty) numeric vector of data values. |
na.rm |
logical. Should missing values be removed? |
... |
The arguments |
Details
The estimator computes both the size
and prob
parameter by default. Be aware
that the likelihood will often be unbounded. According to Olkin et al. (1981),
the likelihood is unbounded when \hat{\mu}/\hat{\sigma}^2 \leq 1
,
where \hat{\sigma}^2
is the biased sample variance. When the likelihood
is unbounded,the maximum likelihood estimator can be regarded as a Poisson
with lambda
parameter equal to the mean of the observation.
When \hat{\mu}/\hat{\sigma}^2 \leq 1
and size
is not supplied by the user,
an error is cast. If size
is provided and size < max(x)
, an error is cast.
The maximum likelihood estimator of size
is unstable, and improvements exist.
See, e.g., Carroll and Lomard (1985) and DasGupta and Rubin (2005).
Value
mlbinom
returns an object of class univariateML
.
This is a named numeric vector with maximum likelihood estimates for
size
and prob
and the following attributes:
model |
The name of the model. |
density |
The density associated with the estimates. |
logLik |
The loglikelihood at the maximum. |
support |
The support of the density. |
n |
The number of observations. |
call |
The call as captured my |
References
Olkin, I., Petkau, A. J., & Zidek, J. V. (1981). A comparison of n Estimators for the binomial distribution. Journal of the American Statistical Association, 76(375), 637-642. https://doi.org/10.1080/01621459.1981.10477697
Johnson, N. L., Kemp, A. W., & Kotz, S. (2005). Univariate Discrete Distributions (3rd ed.). Wiley-Blackwell.
Carroll, R. J., & Lombard, F. (1985). A Note on N Estimators for the Binomial Distribution. Journal of the American Statistical Association, 80(390), 423-426. https://doi.org/10.1080/01621459.1985.10478134
DasGupta, A., & Rubin, H. (2005). Estimation of binomial parameters when both n,p are unknown. Journal of Statistical Planning and Inference, 130(1-2), 391-404. https://doi.org/10.1016/j.jspi.2004.02.019
See Also
Binomial for the density.
Examples
# The likelihood will often be unbounded.
## Not run:
mlbinom(ChickWeight$weight)
## End(Not run)
# Provide a size
mlbinom(ChickWeight$weight, size = 400)
# Or use mlpoiss, the limiting likelihood of the binomial.
mlpois(ChickWeight$weight)