est.kagan {ssEDA}R Documentation

Estimate Parameters of Kagan Distribution

Description

Estimate different parameter or parameters of Kagan distribution for a given data set.

Usage

est.kagan(Data, alpha=1, beta=0, gamma=7, theta=0.75, phi=2.4, tol=10^-3,
          Mag=TRUE, deltam=2)

Arguments

Data Vector of magnitude or stress.
alpha Parameter of Kagan distribution. Index of the power law.
beta Parameter of Kagan distribution. Control the lower turning point of distribution.
gamma Parameter of Kagan distribution. Control the upper turning point of the distribution.
theta Parameter of magnitude.convert.
phi Parameter of magnitude.convert.
tol minimum step length of Newton-Raphson algorithm.
Mag Flag indicating whether stress or magnitude is to be used.
deltam Range for scanning over beta parameter.

Details

Data is given in magnitudes or stress. Under the condition of data following Kagan distribution, parameters of distribution could be estimated, Newton-Raphson algorithm and maximum likelihood method are used here.

Value

Vector of estimated (or fixed) parameters alpha (α), beta (β) and gamma (gamma) of the Kagan distribution, the value of M0 (minimum magnitude) determined from the data and loglikelihood value that those parameters correspond to.

Warning

When the parameters of distribution are all unknown, the estimated results are sometimes not very accurate.

Author(s)

Wang Lifeng, 2001

References

Vere-Jones, D.; Robinson, R. & Yang, W. (2001). Remarks on the accelerated moment release model: problems of model formulation, simulation and estimation. Geophysical Journal International 144, 517–531.

See Also

dkagan

Examples

estimate.alph <- NULL
for (i in 1:100)
{
    # follow Kagan distribution, using default parameters.
    stress <- rkagan(1000, mag = FALSE) # simulate data set of stress which
    # when alpha is unknown.
    alpha <- est.kagan(stress, alpha = NA, Mag = FALSE) # estimate alpha,
    estimate.alph <- rbind(estimate.alph, alpha)
}

# Get distribution of alpha estimated from the 100 samples.  This
# way, we could know possible distance between estimated one
# and real one. 
hist(estimate.alph[, 1], xlab="Alpha", ylab="Frequency", main="")
box()
[Package ssEDA version 2.2-1 Index]