pearson7.fit: Find the MLE for a sample from the Pearson VII distribution...

In pearson7: Maximum Likelihood Inference for the Pearson VII Distribution with Shape Parameter 3/2

Description

Find the MLE for a sample from the Pearson VII distribution with shape parameter 3/2.

Usage

pearson7.fit(y, mu0 = median(y), sigma0 = sqrt(3) * median(abs(y -
  median(y))), tol = 1e-08)

Arguments

y	a vector of observations.
mu0	an initial value for μ.
sigma0	an initial value for σ.
tol	the convergence tolerance.

Details

This function uses a Newton-Raphson algorithm to find the MLE. The starting values for μ and σ are the sample median and √3 times the sample MAD, respectively. See the reference for details.

Value

pearson7.fit returns an object of class “pearson7”, which is a list containing the following components.

theta.hat	the estimates of μ and σ.
hessian	the Hessian matrix evaluated at theta.hat.
iterations	the number of iterations required to attain convergence.
value	the value of the log likelihood at theta.hat.

References

Hughes, J., Shastry, S., Hancock, W. O., and Fricks, J. (2013) Estimating velocity for processive motor proteins with random detachment. Journal of Agricultural, Biological, and Environmental Statistics, in press.

See Also

pearson7.objective

Examples

y = rpearson7(100, 100, 10)
fit = pearson7.fit(y)
fit
summary(fit)

pearson7 documentation built on July 2, 2020, 3:59 a.m.