Bell {countDM} | R Documentation |
MLE of the Bell distribtion
Description
Evaluates the maximum likelihood estimate of the Bell distribtion. The PMF of the Bell distribution is as follows:
where denotes the Bell parameter and
is the Bell number and it is given by
The Bell number in the above equation is the nth moment of the Poisson distribution with parameter equal to 1.
Usage
bell_mle (x)
mle.bell (x, theta)
Arguments
x |
A vector of (non-negative integer) discrete values. |
theta |
A vector of (non-negative integer) values. |
Details
The function allows to estimate the unknown parameter of the Bell distribution with loglik value using a Newton-Raphson algorithm.
Value
bell_mle gives the maximum liklihood estimate of parameter theta. loglik gives value of the maximised log-likelihood. The mle.bell gives the maximum liklihood estimate with standard error and AIC,
Author(s)
Muhammad Imran and M.H. Tahir.
R implementation and documentation: Muhammad Imran imranshakoor84@yahoo.com and M.H. Tahir <mht@iub.edu.pk>.
References
Castellares, F., Ferrari, S. L., & Lemonte, A. J. (2018). On the Bell distribution and its associated regression model for count data. Applied Mathematical Modelling, 56, 172-185.
See Also
Examples
x <- data_sbirth
bell_mle (x)
mle.bell (x, 1.2)