EquilibriumDistribution

final class relife.lifetime_models.EquilibriumDistribution(baseline)

Equilibrium distribution.

The equilibirum distribution is the distribution that makes the renewal process stationnary.

Parameters:

baselineany parametric lifetime model

Lifetime model.

References

[1]

Ross, S. M. (1996). Stochastic stochastic_process. New York: Wiley.

Methods

apply_condition	Return a model with age replacement, left truncation, or both.
cdf	The cumulative distribution function.
chf	The cumulative hazard function.
freeze	Return a model with additional arguments stored.
get_params	Get the parameters of this model.
hf	The hazard function.
ichf	Inverse cumulative hazard function.
is_fitted	Whether fitting results are set.
is_parametrized	Whether at least one parameter value is set.
isf	The inverse survival function.
ls_integrate	Lebesgue-Stieltjes integration.
mean	The mean of the distribution.
median	The median.
moment	The n-th order moment.
mrl	The mean residual life function.
pdf	The probability density function.
plot	Plot function.
ppf	The percent point function, inverse of the CDF.
rvs	Random variate sampling.
set_params	Set the parameters of this model.
sf	The survival function.
var	The variance of the distribution.

apply_condition(*, ar=None, a0=None)

Return a model with age replacement, left truncation, or both.

Parameters:

arfloat or ndarray, optional

Age replacement threshold.

a0float or ndarray, optional

Initial age for left truncation.

Returns:

outParametricLifetimeModel

Conditioned lifetime model.

property args_shape

Shape of additional model arguments.

cdf(time, *args)

The cumulative distribution function.

Parameters:

timefloat or np.ndarray

Elapsed time value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

cdf values at each given time(s).

chf(time, *args)

The cumulative hazard function.

Parameters:

timefloat or np.ndarray

Elapsed time value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

chf values at each given time(s).

freeze(*args)

Return a model with additional arguments stored.

get_params()

Get the parameters of this model.

Returns:

out1darray of floats

Model parameters.

Notes

If parameter values are not set, they default to np.nan values.

hf(time, *args)

The hazard function.

Parameters:

timefloat or np.ndarray

Elapsed time value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

hf values at each given time(s).

ichf(cumulative_hazard_rate, *args)

Inverse cumulative hazard function.

Parameters:

cumulative_hazard_ratefloat or np.ndarray

Cumulative hazard rate value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

ichf values at each given cumulative hazard rate(s).

is_fitted()

Whether fitting results are set.

is_parametrized()

Whether at least one parameter value is set.

isf(probability, *args)

The inverse survival function.

Parameters:

probabilityfloat or np.ndarray

Probability value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

isf values at each given probability value(s).

ls_integrate(func, a, b, *density_args, func_args=(), deg=10)

Lebesgue-Stieltjes integration.

Parameters:

funcCallable

Function to integrate with respect to the lifetime distribution.

afloat or ndarray

Lower bound of the integration.

bfloat or ndarray

Upper bound of the integration.

*density_args

Additional arguments required by the lifetime model.

func_argstuple, default=()

Additional arguments required by func.

degint, default=10

Number of sample points and weights for the quadrature.

Returns:

outnp.ndarray

Lebesgue-Stieltjes integration of func from a to b.

mean(*args)

The mean of the distribution.

Parameters:

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

median(*args)

The median.

Parameters:

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

moment(n, *args)

The n-th order moment.

Parameters:

nint

Order of the moment, at least 1.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

mrl(time, *args)

The mean residual life function.

Parameters:

timefloat or np.ndarray

Elapsed time value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

Function values at each given time(s).

pdf(time, *args)

The probability density function.

Parameters:

timefloat or np.ndarray

Elapsed time value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

pdf values at each given time(s).

plot(fname, time, *args, ax=None, **kwargs)

Plot function.

Parameters:

fnamestr

The function name to plot. Allowed names are sf, cdf, chf, hf, pdf.

time1d array

The timeline used for x-axis.

*args

Any additional args required to compute the function.

axplt.Axes, optional

An optional existing matplotlib.axes.

**kwargs

Extra arguments to configure the plot:

• ci : bool, default is True if the model has fitting_results

• alpha_ci :

• any arguments allowed by matplotlib.plot

ppf(probability, *args)

The percent point function, inverse of the CDF.

Parameters:

probabilityfloat or np.ndarray

Probability value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

ppf values at each given probability value(s).

rvs(size=None, *args, seed=None)

Random variate sampling.

Parameters:

sizeint or tuple (m, n) of int

Size of the generated sample.

*args

Any additional args.

seedoptional int, np.random.BitGenerator, np.random.Generator, np.random.RandomState, default is None

If int or BitGenerator, seed for random number generator. If np.random.RandomState or np.random.Generator, use as given.

Returns:

outfloat or ndarray

Sample values.

set_params(new_params)

Set the parameters of this model.

Parameters:

new_params1d array-like of floats

Model parameters.

Notes

set_params definition expects an array-like of floats. At runtime, complex parameters might be setted temporarily to approximate fitted parameters covariance. This is contradictory to the given typing. At the moment, we don’t see a better solution and we believe that this is actually a limitation of what can be expressed in the static typesystem.

sf(time, *args)

The survival function.

Parameters:

timefloat or np.ndarray

Elapsed time value(s) at which to compute the function.

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray

sf values at each given time(s).

var(*args)

The variance of the distribution.

Parameters:

*args

Any additional args.

Returns:

outnp.float64 or np.ndarray