ExponentialErrorDistribution

ExponentialErrorDistribution = class ExponentialErrorDistribution(ScaledErrorDistribution)

ExponentialErrorDistribution(scale=1.0, power=2.0, limits=None, copy=None) Also known as generalized gaussian errordistribution. To calculate an Exponential likelihood. For one residual, x, it holds f( x ) = p / ( 2 s Γ( 1 / p ) ) exp( - ( |x| / s ) ^ p ) where s is the scale and p is the power. s and p are hyperparameters, which might be estimated from the data. The variance of this function is σ ^ 2 = s ^ 2 Γ( 3 / p ) / Γ( 1 / p ) See toSigma() The function is mostly used to calculate the likelihood L over N residuals, or easier to use log( L ) logL = log( N p / ( 2 s Γ( 1 / p ) ) ) - ∑( ( |x| / s ) ^ p ) Using weights this becomes: logL = log( ∑( w ) p / ( 2 s Γ( 1 / p ) ) ) - ∑( w ( |x| / s ) ^ p ) Note ---- The scale s in Exponential is NOT the same as the scale in Gaussian or in Laplace. Attributes from ErrorDistibution -------------------------------- hyperpar, deltaP, ncalls, nparts, sumweight, ndata, hypar, nphypar Author Do Kester.

Method resolution order:: ExponentialErrorDistribution; ScaledErrorDistribution; ErrorDistribution; builtins.object

Constructor:

ExponentialErrorDistribution( scale=1.0, power=2.0, limits=None, copy=None ): Default Constructor. Parameters ---------- scale : float noise scale power : float power of the distribution limits : None or [low,high] or [[low],[high]] None : no limits implying fixed scale low low limit on scale (needs to be >0) high high limit on scale [low] low limit on [scale,power] (need to be >0) [high] high limit on [scale,power] when limits are set, the scale cq. power are *not* fixed. copy : ExponentialErrorDistribution distribution to be copied.

Methods defined here:

acceptWeight(): True if the distribution accepts weights. Always true for this distribution.

copy(): Return copy of this.

getChipow( problem, allpars=None, scale=1): Return chisq. return Sum over the (weighted) powered residuals Parameters ---------- problem : Problem to be solved allpars : array_like None take parameters from problem.model list of all parameters in the problem scale : float or array_like present scale

getScale( problem, allpars=None ): Return the noise scale calculated from the residuals. Parameters ---------- problem : Problem to be solved allpars : array_like None take parameters from problem.model list of all parameters in the problem

logLdata( problem, allpars, mockdata=None ): Return the log( likelihood ) for each residual logL = sum( logLdata ) Parameters ---------- problem : Problem to be solved allpars : array_like list of all parameters in the problem mockdata : array_like as calculated by the model

logLikelihood_alt( problem, allpars ): Return the log( likelihood ) for a Gaussian distribution. Parameters ---------- problem : Problem to be solved allpars : array_like parameters of the problem

nextPartialData( problem, allpars, fitIndex, mockdata=None ): Return the partial derivative of all elements of the log( likelihood ) to the parameters. dL/ds is not implemented for problems with accuracy Parameters ---------- problem : Problem to be solved allpars : array_like parameters of the problem fitIndex : array_like indices of parameters to be fitted mockdata : array_like as calculated by the model

partialLogL_alt( problem, allpars, fitIndex ): Return the partial derivative of log( likelihood ) to the parameters. dL/ds is not implemented for problems with accuracy Parameters ---------- problem : Problem to be solved allpars : array_like parameters of the problem fitIndex : array_like indices of parameters to be fitted

toSigma( hypar ): Return sigma, the squareroot of the variance. Parameter -------- hypar : array_like (2 floats) the [scale,power] of this Exponential distribution.

Methods inherited from ScaledErrorDistribution:

setLimits( limits )

Methods inherited from ErrorDistribution: