pystra.distributions.shiftedlognormal.ShiftedLognormal#

class ShiftedLognormal(name, mean, stdv, lower, input_type=None, startpoint=None)[source]#

Bases: Lognormal

Shifted Lognormal distribution

If X is a lognormal random variable, then Y = X + lower is a shifted lognormal random variable.

Arguments:

name (str): Name of the random variable
mean (float): Mean
stdv (float): Standard deviation
lower (float): Lower bound of the distribution (i.e. the shift applied to the lognormal)
input_type (any): Change meaning of mean and stdv. Not implemented!
startpoint (float): Start point for seach

Note: Could use scipy to do the heavy lifting. However, there is a small performance hit, so for this common dist use bespoke implementation for the PDF, CDF.

Methods

`cdf`	Cumulative distribution function
`getMean`
`getName`
`getStartPoint`
`getStdv`
`jacobian`	Compute the Jacobian
`pdf`	Probability density function Note: asssumes x>lower for performance, scipy manages this appropriately
`plot`	Plots the PDF of the distribution
`ppf`	Inverse cumulative distribution function
`sample`	Return a sample of the distribution of length n
`setStartPoint`
`set_location`	Updating the distribution location parameter.
`set_lower`	Updating the distribution lower parameter.
`set_scale`	Updating the distribution scale parameter.
`u_to_x`	Transformation from u to x
`x_to_u`	Transformation from x to u Note: asssumes x>lower for performance

Attributes

std_normal

pdf(x)[source]#: Probability density function Note: asssumes x>lower for performance, scipy manages this appropriately

cdf(x)[source]#: Cumulative distribution function

u_to_x(u)[source]#: Transformation from u to x

x_to_u(x)[source]#: Transformation from x to u Note: asssumes x>lower for performance

set_lower(lower=0)[source]#: Updating the distribution lower parameter. For Lognormal, even though we have a SciPy object, it’s not being used in the functions above for performance, so we need to update params directly.

jacobian(u, x)#: Compute the Jacobian

plot(ax=None, **kwargs)#: Plots the PDF of the distribution

ppf(u)#: Inverse cumulative distribution function

sample(n=1000)#: Return a sample of the distribution of length n

set_location(loc=0)#: Updating the distribution location parameter. For Lognormal, even though we have a SciPy object, it’s not being used in the functions above for performance, so we need to update pe.arams directly.

set_scale(scale=1)#: Updating the distribution scale parameter. For Lognormal, even though we have a SciPy object, it’s not being used in the functions above for performance, so we need to update params directly.