Estimates the parameters of a hyperbolic distribution.

## Usage

hypFit(x, alpha = 1, beta = 0, delta = 1, mu = 0,
scale = TRUE, doplot = TRUE, span = "auto", trace = TRUE,
title = NULL, description = NULL, ...)

## Arguments

x

a numeric vector.

alpha

shape parameter, a positive number.

beta

skewness parameter, abs(beta) is in the range (0, alpha).

delta

scale parameter, must be zero or positive.

mu

location parameter, by default 0.

scale

a logical flag, by default TRUE. Should the time series be scaled by its standard deviation to achieve a more stable optimization?

doplot

a logical flag. Should a plot be displayed?

span

x-coordinates for the plot, by default 100 values automatically selected and ranging between the 0.001, and 0.999 quantiles. Alternatively, you can specify the range by an expression like span=seq(min, max, times = n), where, min and max are the left and right endpoints of the range, and n gives the number of the intermediate points.

trace

a logical flag. Should the parameter estimation process be traced?

title

a character string which allows for a project title.

description

a character string which allows for a brief description.

...

parameters to be parsed.

## Details

The meaning of the parameters given above corresponds to the first parameterization, see dhyp for details.

The function nlm is used to minimize the "negative" maximum log-likelihood function. nlm carries out a minimization using a Newton-type algorithm.

## Value

an object from class "fDISTFIT". Slot fit is a list with the following components:

estimate

the point at which the maximum value of the log liklihood function is obtained.

minimum

the value of the estimated maximum, i.e. the value of the log liklihood function.

code

an integer indicating why the optimization process terminated.
1: relative gradient is close to zero, current iterate is probably solution;
2: successive iterates within tolerance, current iterate is probably solution;
3: last global step failed to locate a point lower than estimate. Either estimate is an approximate local minimum of the function or steptol is too small;
4: iteration limit exceeded;
5: maximum step size stepmax exceeded five consecutive times. Either the function is unbounded below, becomes asymptotic to a finite value from above in some direction or stepmax is too small.

the gradient at the estimated maximum.

steps

number of function calls.

## Examples

## rhyp -
# Simulate Random Variates:
set.seed(1953)
s = rhyp(n = 1000, alpha = 1.5, beta = 0.3, delta = 0.5, mu = -1.0)

## hypFit -
# Fit Parameters:
hypFit(s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE)
#>
#>  Objective Function Value:   -1508.093
#>  Parameter Estimates:        1 0 1 -0.6991407
#>
#>  Objective Function Value:   -1508.093
#>  Parameter Estimates:        1 0 1 -0.6991407
#>
#>  Objective Function Value:   -1508.093
#>  Parameter Estimates:        1 1.490116e-08 1 -0.6991407
#>
#>  Objective Function Value:   -1508.093
#>  Parameter Estimates:        1 0 1 -0.6991407
#>
#>  Objective Function Value:   -1508.093
#>  Parameter Estimates:        1 0 1 -0.6991406
#>
#>  Objective Function Value:   -1378.357
#>  Parameter Estimates:        1.939637 0.1591279 0.700799 -0.6518213
#>
#>  Objective Function Value:   -1378.355
#>  Parameter Estimates:        1.939602 0.1591279 0.700799 -0.6518213
#>
#>  Objective Function Value:   -1378.353
#>  Parameter Estimates:        1.939637 0.1590929 0.700799 -0.6518213
#>
#>  Objective Function Value:   -1378.356
#>  Parameter Estimates:        1.939637 0.1591279 0.700834 -0.6518213
#>
#>  Objective Function Value:   -1378.35
#>  Parameter Estimates:        1.939637 0.1591279 0.700799 -0.6518563
#>
#>  Objective Function Value:   -2163.307
#>  Parameter Estimates:        1.862755 -0.3304589 0.7430581 -1.519351
#>
#>  Objective Function Value:   -1365.864
#>  Parameter Estimates:        1.922406 0.1038927 0.7082374 -0.7475008
#>
#>  Objective Function Value:   -1365.864
#>  Parameter Estimates:        1.922408 0.1038927 0.7082374 -0.7475008
#>
#>  Objective Function Value:   -1365.864
#>  Parameter Estimates:        1.922406 0.1038969 0.7082374 -0.7475008
#>
#>  Objective Function Value:   -1365.864
#>  Parameter Estimates:        1.922406 0.1038927 0.7082319 -0.7475008
#>
#>  Objective Function Value:   -1365.864
#>  Parameter Estimates:        1.922406 0.1038927 0.7082374 -0.7474973
#>
#>  Objective Function Value:   -1363.818
#>  Parameter Estimates:        1.835478 0.1679592 0.7371946 -0.7551355
#>
#>  Objective Function Value:   -1363.818
#>  Parameter Estimates:        1.835504 0.1679592 0.7371946 -0.7551355
#>
#>  Objective Function Value:   -1363.818
#>  Parameter Estimates:        1.835478 0.1679579 0.7371946 -0.7551355
#>
#>  Objective Function Value:   -1363.818
#>  Parameter Estimates:        1.835478 0.1679592 0.7371653 -0.7551355
#>
#>  Objective Function Value:   -1363.818
#>  Parameter Estimates:        1.835478 0.1679592 0.7371946 -0.7551345
#>
#>  Objective Function Value:   -1363.158
#>  Parameter Estimates:        1.806576 0.171103 0.6890099 -0.8520412
#>
#>  Objective Function Value:   -1363.158
#>  Parameter Estimates:        1.806579 0.171103 0.6890099 -0.8520412
#>
#>  Objective Function Value:   -1363.158
#>  Parameter Estimates:        1.806576 0.1711045 0.6890099 -0.8520412
#>
#>  Objective Function Value:   -1363.158
#>  Parameter Estimates:        1.806576 0.171103 0.6890137 -0.8520412
#>
#>  Objective Function Value:   -1363.158
#>  Parameter Estimates:        1.806576 0.171103 0.6890099 -0.8520397
#>
#>  Objective Function Value:   -1360.109
#>  Parameter Estimates:        1.769539 0.2437448 0.6121537 -0.8505328
#>
#>  Objective Function Value:   -1360.109
#>  Parameter Estimates:        1.769547 0.2437448 0.6121537 -0.8505328
#>
#>  Objective Function Value:   -1360.109
#>  Parameter Estimates:        1.769539 0.2437435 0.6121537 -0.8505328
#>
#>  Objective Function Value:   -1360.109
#>  Parameter Estimates:        1.769539 0.2437448 0.6121661 -0.8505328
#>
#>  Objective Function Value:   -1360.109
#>  Parameter Estimates:        1.769539 0.2437448 0.6121537 -0.8505338
#>
#>  Objective Function Value:   -1359.169
#>  Parameter Estimates:        1.710098 0.2401547 0.5182934 -0.8647414
#>
#>  Objective Function Value:   -1359.169
#>  Parameter Estimates:        1.710105 0.2401547 0.5182934 -0.8647414
#>
#>  Objective Function Value:   -1359.169
#>  Parameter Estimates:        1.710098 0.2401559 0.5182934 -0.8647414
#>
#>  Objective Function Value:   -1359.169
#>  Parameter Estimates:        1.710098 0.2401547 0.5183074 -0.8647414
#>
#>  Objective Function Value:   -1359.169
#>  Parameter Estimates:        1.710098 0.2401547 0.5182934 -0.8647403
#>
#>  Objective Function Value:   -1358.59
#>  Parameter Estimates:        1.636735 0.2050391 0.4571394 -0.8178077
#>
#>  Objective Function Value:   -1358.59
#>  Parameter Estimates:        1.636742 0.2050391 0.4571394 -0.8178077
#>
#>  Objective Function Value:   -1358.59
#>  Parameter Estimates:        1.636735 0.2050375 0.4571394 -0.8178077
#>
#>  Objective Function Value:   -1358.59
#>  Parameter Estimates:        1.636735 0.2050391 0.4571449 -0.8178077
#>
#>  Objective Function Value:   -1358.59
#>  Parameter Estimates:        1.636735 0.2050391 0.4571394 -0.8178089
#>
#>  Objective Function Value:   -1358.387
#>  Parameter Estimates:        1.575816 0.1632939 0.3729416 -0.8139854
#>
#>  Objective Function Value:   -1358.387
#>  Parameter Estimates:        1.575812 0.1632939 0.3729416 -0.8139854
#>
#>  Objective Function Value:   -1358.387
#>  Parameter Estimates:        1.575816 0.1632957 0.3729416 -0.8139854
#>
#>  Objective Function Value:   -1358.387
#>  Parameter Estimates:        1.575816 0.1632939 0.3729485 -0.8139854
#>
#>  Objective Function Value:   -1358.387
#>  Parameter Estimates:        1.575816 0.1632939 0.3729416 -0.8139843
#>
#>  Objective Function Value:   -1358.081
#>  Parameter Estimates:        1.558526 0.2320373 0.2939126 -0.8498682
#>
#>  Objective Function Value:   -1358.081
#>  Parameter Estimates:        1.558531 0.2320373 0.2939126 -0.8498682
#>
#>  Objective Function Value:   -1358.081
#>  Parameter Estimates:        1.558526 0.232036 0.2939126 -0.8498682
#>
#>  Objective Function Value:   -1358.081
#>  Parameter Estimates:        1.558526 0.2320373 0.2939194 -0.8498682
#>
#>  Objective Function Value:   -1358.081
#>  Parameter Estimates:        1.558526 0.2320373 0.2939126 -0.8498694
#>
#>  Objective Function Value:   -1360.764
#>  Parameter Estimates:        1.496882 0.2542706 0.3816928 -0.8734914
#>
#>  Objective Function Value:   -1358.026
#>  Parameter Estimates:        1.553858 0.2249425 0.3012205 -0.8496544
#>
#>  Objective Function Value:   -1358.026
#>  Parameter Estimates:        1.553865 0.2249425 0.3012205 -0.8496544
#>
#>  Objective Function Value:   -1358.026
#>  Parameter Estimates:        1.553858 0.2249441 0.3012205 -0.8496544
#>
#>  Objective Function Value:   -1358.026
#>  Parameter Estimates:        1.553858 0.2249425 0.3012147 -0.8496544
#>
#>  Objective Function Value:   -1358.026
#>  Parameter Estimates:        1.553858 0.2249425 0.3012205 -0.8496522
#>
#>  Objective Function Value:   -1358.026
#>  Parameter Estimates:        1.553858 0.2249425 0.3012205 -0.8496566
#>
#>  Objective Function Value:   -1358.037
#>  Parameter Estimates:        1.551868 0.2251994 0.3062864 -0.8398621
#>
#>  Objective Function Value:   -1358.01
#>  Parameter Estimates:        1.552992 0.2250544 0.3034259 -0.8453915
#>
#>  Objective Function Value:   -1358.01
#>  Parameter Estimates:        1.552995 0.2250544 0.3034259 -0.8453915
#>
#>  Objective Function Value:   -1358.01
#>  Parameter Estimates:        1.552992 0.2250564 0.3034259 -0.8453915
#>
#>  Objective Function Value:   -1358.01
#>  Parameter Estimates:        1.552992 0.2250524 0.3034259 -0.8453915
#>
#>  Objective Function Value:   -1358.01
#>  Parameter Estimates:        1.552992 0.2250544 0.3034219 -0.8453915
#>
#>  Objective Function Value:   -1358.01
#>  Parameter Estimates:        1.552992 0.2250544 0.3034259 -0.8453928
#>
#>  Objective Function Value:   -1357.998
#>  Parameter Estimates:        1.553334 0.2206549 0.3053404 -0.8462044
#>
#>  Objective Function Value:   -1357.998
#>  Parameter Estimates:        1.553331 0.2206549 0.3053404 -0.8462044
#>
#>  Objective Function Value:   -1357.998
#>  Parameter Estimates:        1.553334 0.2206562 0.3053404 -0.8462044
#>
#>  Objective Function Value:   -1357.998
#>  Parameter Estimates:        1.553334 0.2206549 0.3053366 -0.8462044
#>
#>  Objective Function Value:   -1357.998
#>  Parameter Estimates:        1.553334 0.2206549 0.3053404 -0.8462035
#>
#>  Objective Function Value:   -1357.987
#>  Parameter Estimates:        1.553236 0.2201545 0.3072669 -0.8417517
#>
#>  Objective Function Value:   -1357.987
#>  Parameter Estimates:        1.553239 0.2201545 0.3072669 -0.8417517
#>
#>  Objective Function Value:   -1357.987
#>  Parameter Estimates:        1.553236 0.2201553 0.3072669 -0.8417517
#>
#>  Objective Function Value:   -1357.987
#>  Parameter Estimates:        1.553236 0.2201536 0.3072669 -0.8417517
#>
#>  Objective Function Value:   -1357.987
#>  Parameter Estimates:        1.553236 0.2201545 0.3072629 -0.8417517
#>
#>  Objective Function Value:   -1357.987
#>  Parameter Estimates:        1.553236 0.2201545 0.3072669 -0.8417527
#>
#>  Objective Function Value:   -1357.977
#>  Parameter Estimates:        1.554475 0.2157089 0.3088434 -0.8416293
#>
#>  Objective Function Value:   -1357.977
#>  Parameter Estimates:        1.554471 0.2157089 0.3088434 -0.8416293
#>
#>  Objective Function Value:   -1357.977
#>  Parameter Estimates:        1.554475 0.2157102 0.3088434 -0.8416293
#>
#>  Objective Function Value:   -1357.977
#>  Parameter Estimates:        1.554475 0.2157089 0.3088394 -0.8416293
#>
#>  Objective Function Value:   -1357.977
#>  Parameter Estimates:        1.554475 0.2157089 0.3088434 -0.8416284
#>
#>  Objective Function Value:   -1357.968
#>  Parameter Estimates:        1.555687 0.2149972 0.3122155 -0.8383965
#>
#>  Objective Function Value:   -1357.968
#>  Parameter Estimates:        1.55569 0.2149972 0.3122155 -0.8383965
#>
#>  Objective Function Value:   -1357.968
#>  Parameter Estimates:        1.555687 0.2149961 0.3122155 -0.8383965
#>
#>  Objective Function Value:   -1357.968
#>  Parameter Estimates:        1.555687 0.2149972 0.3122117 -0.8383965
#>
#>  Objective Function Value:   -1357.968
#>  Parameter Estimates:        1.555687 0.2149972 0.3122155 -0.8383976
#>
#>  Objective Function Value:   -1357.962
#>  Parameter Estimates:        1.556302 0.2144107 0.3167415 -0.8400066
#>
#>  Objective Function Value:   -1357.962
#>  Parameter Estimates:        1.556306 0.2144107 0.3167415 -0.8400066
#>
#>  Objective Function Value:   -1357.962
#>  Parameter Estimates:        1.556302 0.2144119 0.3167415 -0.8400066
#>
#>  Objective Function Value:   -1357.962
#>  Parameter Estimates:        1.556302 0.2144107 0.3167369 -0.8400066
#>
#>  Objective Function Value:   -1357.962
#>  Parameter Estimates:        1.556302 0.2144107 0.3167415 -0.8400057
#>
#>  Objective Function Value:   -1357.957
#>  Parameter Estimates:        1.5589 0.2131744 0.3201281 -0.8379938
#>
#>  Objective Function Value:   -1357.957
#>  Parameter Estimates:        1.558904 0.2131744 0.3201281 -0.8379938
#>
#>  Objective Function Value:   -1357.957
#>  Parameter Estimates:        1.558896 0.2131744 0.3201281 -0.8379938
#>
#>  Objective Function Value:   -1357.957
#>  Parameter Estimates:        1.5589 0.2131765 0.3201281 -0.8379938
#>
#>  Objective Function Value:   -1357.957
#>  Parameter Estimates:        1.5589 0.2131723 0.3201281 -0.8379938
#>
#>  Objective Function Value:   -1357.957
#>  Parameter Estimates:        1.5589 0.2131744 0.3201247 -0.8379938
#>
#>  Objective Function Value:   -1357.957
#>  Parameter Estimates:        1.5589 0.2131744 0.3201281 -0.8379948
#>
#>  Objective Function Value:   -1357.954
#>  Parameter Estimates:        1.559259 0.2120718 0.3248605 -0.8377534
#>
#>  Objective Function Value:   -1357.954
#>  Parameter Estimates:        1.559262 0.2120718 0.3248605 -0.8377534
#>
#>  Objective Function Value:   -1357.954
#>  Parameter Estimates:        1.559259 0.2120735 0.3248605 -0.8377534
#>
#>  Objective Function Value:   -1357.954
#>  Parameter Estimates:        1.559259 0.2120718 0.324857 -0.8377534
#>
#>  Objective Function Value:   -1357.954
#>  Parameter Estimates:        1.559259 0.2120718 0.3248605 -0.8377485
#>
#>  Objective Function Value:   -1357.954
#>  Parameter Estimates:        1.559259 0.2120718 0.3248605 -0.8377583
#>
#>  Objective Function Value:   -1357.954
#>  Parameter Estimates:        1.562143 0.2092982 0.3274369 -0.8366801
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560588 0.2110467 0.3257805 -0.836658
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560586 0.2110467 0.3257805 -0.836658
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560588 0.211048 0.3257805 -0.836658
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560588 0.2110453 0.3257805 -0.836658
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560588 0.2110467 0.3257821 -0.836658
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560588 0.2110467 0.3257789 -0.836658
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560588 0.2110467 0.3257805 -0.8366591
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560479 0.210568 0.3277645 -0.83583
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560493 0.210568 0.3277645 -0.83583
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560465 0.210568 0.3277645 -0.83583
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560479 0.2105716 0.3277645 -0.83583
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560479 0.2105645 0.3277645 -0.83583
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560479 0.210568 0.3277619 -0.83583
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560479 0.210568 0.3277645 -0.835828
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.560479 0.210568 0.3277645 -0.8358321
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.561781 0.2102193 0.329437 -0.836328
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.561779 0.2102193 0.329437 -0.836328
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.561781 0.210221 0.329437 -0.836328
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.561781 0.2102193 0.3294422 -0.836328
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.561781 0.2102193 0.3294318 -0.836328
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.561781 0.2102193 0.329437 -0.8363268
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563285 0.2112439 0.3306011 -0.8367706
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563287 0.2112439 0.3306011 -0.8367706
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563283 0.2112439 0.3306011 -0.8367706
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563285 0.2112449 0.3306011 -0.8367706
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563285 0.2112429 0.3306011 -0.8367706
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563285 0.2112439 0.3306142 -0.8367706
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563285 0.2112439 0.3305879 -0.8367706
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563285 0.2112439 0.3306011 -0.8367699
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563285 0.2112439 0.3306011 -0.8367713
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563058 0.210519 0.3306562 -0.8361201
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563079 0.210519 0.3306562 -0.8361201
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563036 0.210519 0.3306562 -0.8361201
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563058 0.210528 0.3306562 -0.8361201
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563058 0.21051 0.3306562 -0.8361201
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563058 0.210519 0.330682 -0.8361201
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563058 0.210519 0.3306303 -0.8361201
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563058 0.210519 0.3306562 -0.8361185
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563058 0.210519 0.3306562 -0.8361217
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563019 0.2105828 0.3305017 -0.8362043
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56304 0.2105828 0.3305017 -0.8362043
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.562997 0.2105828 0.3305017 -0.8362043
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563019 0.210593 0.3305017 -0.8362043
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563019 0.2105727 0.3305017 -0.8362043
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563019 0.2105828 0.3305208 -0.8362043
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563019 0.2105828 0.3304826 -0.8362043
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563019 0.2105828 0.3305017 -0.8361996
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563019 0.2105828 0.3305017 -0.8362091
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56303 0.2105901 0.3305431 -0.8362097
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563059 0.2105901 0.3305431 -0.8362097
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.563 0.2105901 0.3305431 -0.8362097
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56303 0.2106117 0.3305431 -0.8362097
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56303 0.2105685 0.3305431 -0.8362097
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56303 0.2105901 0.3305803 -0.8362097
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56303 0.2105901 0.3305059 -0.8362097
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56303 0.2105901 0.3305431 -0.8361901
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56303 0.2105901 0.3305431 -0.8362293
#>
#>  Objective Function Value:   -1357.952
#>  Parameter Estimates:        1.56303 0.2105901 0.3305431 -0.8362097
#>
#>  Objective Function Value:   -1453.683
#>  Parameter Estimates:        1.420338 0.191365 0.3637505 -0.920218

#>
#> Title:
#>  Hyperbolic Parameter Estimation
#>
#> Call:
#>  hypFit(x = s, alpha = 1, beta = 0, delta = 1, mu = mean(s), doplot = TRUE)
#>
#> Model:
#>  Hyperbolic Distribution
#>
#> Estimated Parameter(s):
#>      alpha       beta      delta         mu
#>  1.4203380  0.1913650  0.3637505 -0.9202180
#>