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fit with cdf of skew normal distriubtion

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Tom Pether

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Sep 1, 2010, 6:27:39 AM9/1/10

Hi,

to am trying to fit the integral of the skew normal distribution to a
set of data. xhis is my fit function:

upperlimit[x_, y0_, p2_, a_] = p2 (1 - (x/y0)^(1/a));
f[x_, y0_, a_, p2_, s_, skew_, A_, b_, p_] :=
b - 2 A NIntegrate[
PDF[NormalDistribution[p, s], x] CDF[
NormalDistribution[p*skew, s], (skew*x)], {x, -100,
uperlimit[x, y0, p2, a]}, MaxPoints -> 200, MaxRecursion -> 6,
PrecisionGoal -> 4];

then i call the fit by

FitResult =
NonlinearModelFit[data, f[x, y0, a, p2, s, skew, A, b, p], init,
{index, t},
Weights -> weights, VarianceEstimatorFunction -> Automatic,
PrecisionGoal -> 4];

if i then want to get error estimates for the fit parameters by calling

FitResult["ParameterTable"]

i get the following error messages (and no error estimates):

General::stop: Further output of NIntegrate::nlim will be suppressed
during this calculation. >>

Function::slotn: Slot number 2 in
FittedModels`NonlinearFitDump`cnf[{T0,a,pc,s,skew},<<1>>,{},Sequence@@{WorkingPrecision->MachinePrecision}]/.FittedModels`NonlinearFitDump`cnf-><<36>>&
cannot be filled from (<<1>>)[##1]. >>

Power::infy: Infinite expression 1/0. encountered. >>

General::stop: Further output of Power::infy will be suppressed during
this calculation. >>

\[Infinity]::indet: Indeterminate expression 0. ComplexInfinity
encountered. >>

General::stop: Further output of \[Infinity]::indet will be suppressed
during this calculation. >>

does anybody have any idea how to fix this? if i do a fit with
CDF[NormalDistribution...] it works well. with my "self made" CDF f[] it
doesn't... i am stuck here. thanks in advance

tom

Ray Koopman

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Sep 3, 2010, 6:06:52 AM9/3/10

On Sep 1, 3:27 am, Tom Pether <peth...@googlemail.com> wrote:
> Hi,
>
> to am trying to fit the integral of the skew normal distribution to a
> set of data. xhis is my fit function:

Why are you doing least-squares fitting to the cdf? Why not get
initial estimates by fitting the first three moments of the data,
and then use maximum likelihood to get better estimates?

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