pwmdist package

The package consists of functions related to generalized pareto distribution.

gpdpwmFit module

The ‘gpdpwmFit’ module aims to fit a given set of data with generalized pareto distribution using probability weighted moments to calculate the parameter esimates. The package also provides an estimate of Risk measures.

pwmdist.gpdpwmFit.Fitbygpdpwm(data, ci=0.95, threshold=None)

1) Description: The function fits Generalized pareto distiribution to the passed dataset; a timeseries object using probability weighted moments method.

2. Input Parameters:

   data: timeseries dataframe. ci: confidence interval threshold: A float, A threshold number obtained from Peak over threshold method If the threshold value is passed than the manual threshold value is used else the quantile at a given confidence interval is used to calculate the threshold.

3. Results:

   The function returns a dicitionary, which has data, list of residuals, probability, shape parameter, scale parameter, list of exceedances (case where data[i]>threshold), threshold value, excess(case in exceedances subtracted from threshold.) This result dictionary can be used in the plot functions

4. Example:

   the example of the “data” parameter is as follows: Date log(return) 25-12-2020 0.11098978 26-12-2020 0.14787224

pwmdist.gpdpwmFit.depd(x, location=0, scale=1, shape=0, log=False)

1. Description:

   Density for the Generalized Pareto distribution function

2. Input parameters:

   scale, location, shape: parameters of GPD x is the data element obtained from Fitbygpdpwm function log= by default False

3. Example:

   fit=Fitbygpdpwm(dataframe, ci=0.95, threshold=None) depd(fit[‘data’], location, scale=fit[‘scale’],shape= fit[‘shape’], log=False)

pwmdist.gpdpwmFit.gpdMoments(shape=1, location=0, scale=1)

1. Description: Compute true statistics for Generalized Pareto distribution

2. Input parameter:

   shape, location, scale parameters from generalized pareto distribution

3. Value:

Returns true mean of Generalized Pareto distribution for xi < 1 else NaN Returns true variance of Generalized Pareto distribution for xi < 1 else NaN

pwmdist.gpdpwmFit.gpdSimulation(shape=0.25, location=0, scale=1, n=1000, seed=None)

1. Description: Generates random variates from a GPD distribution

2. Input parameters:

   shape, location, scale = the parameter estimates that can be either manually input or taken from Fitbygpdpwm function n = number of simulated observations seed = by default None

3. Result:

   list of simulate values from generalized pareto distribution

pwmdist.gpdpwmFit.gpdpwmFitCheck(data, ci=0.95, threshold=None)

1. Description:

   Checks the Fit of GPD with probability weighted moments

2. Input Parameters:

   data= timeseries dataframe

   ci= confidence interval

   threhsold=A float, A threshold number obtained from Peak over threshold method If the threshold value is passed than the manual threshold value is used else the quantile at a given confidence interval is used to calculate the threshold.

3. Results:

   A dictionary of parameter estimates, threshold and excess.

pwmdist.gpdpwmFit.pgpd(q, location=0, scale=1, shape=1, lowertail=True)

1. Description:

   Probability for the Generalized Pareto distribution function

2. Input parameters:

   scale, location, shape: parameters of GPD lowertail = by default True

pwmdist.gpdpwmFit.qgpd(p, location=0, scale=1, shape=1, lowertail=True)

1. Description:

   Quantiles for the Generalized Pareto distribution function

2. Input parameters:

   scale, location, shape: parameters of GPD lowertail = by default True

gpdplots module

The ‘gpdplots’ module aims to provide a pictoral view of tail of the distribution, emperical distribution, quantile function plot and tails etimates as of now.

pwmdist.gpdplots.disttail(obj, labels=True)

1. Description: Tail of Underlying Distribution

2. Arguments:

   x - an object of class fGPDFIT labels - a logical flag. Should labels be printed?

3. Example:

   obj= Fitbygpdpwm(data, ci, threshold) disttail(obj)

pwmdist.gpdplots.empericalplt(obj, labels=True)

1. Description:

   Empirical Distribution Plot

2. Input parameters:

   obj = Fitbygpdpwm function output labels = By default True

3. Example:

   obj= Fitbygpdpwm(data, ci, threshold) empericalplt(obj)

pwmdist.gpdplots.residualplot(obj, labels=True)

1)Description:

Quantile-Quantile Plot of GPD Residuals

2. Arguments:

   obj = Fitbygpdpwm function output labels - a logical flag. checks if labels should be printed.

3. Example:

   obj = Fitbygpdpwm(data, ci, threshold) residualplot(obj)

pwmdist.gpdplots.tailestimategpd(obj, labels=True)

1. Description:

   Plots tail estimate from GPD model

2. Arguments:

   obj = Fitbygpdpwm function output labels = By default True

3. Example:

   obj= Fitbygpdpwm(data, ci, threshold) tailestimategpd(obj)