AgeReplacementModel#

class relife.lifetime_models.AgeReplacementModel(baseline)[source]#

Age replacement model.

Lifetime model where the assets are replaced at age \(a_r\). This is equivalent to the model of \(\min(X,a_r)\) where \(X\) is a baseline lifetime and \(a_r\) is the age of replacement.

Parameters:

baselineany parametric lifetime model (frozen lifetime model works): The base lifetime model without conditional probabilities

Attributes:

baseline
nb_params
params
params_names
plot

Methods

`cdf`	The cumulative density function.
`chf`	The cumulative hazard function.
`freeze`	Freeze age replacement values and other arguments into the object data.
`get_params`	Get the parameters of this model.
`get_params_names`	Parameters names.
`hf`	The hazard function.
`ichf`	Inverse cumulative hazard function.
`isf`	The inverse survival function.
`ls_integrate`	Lebesgue-Stieltjes integration.
`mean`	The mean of the distribution.
`median`	The median.
`moment`	n-th order moment.
`mrl`	The mean residual life function.
`pdf`	The probability density function.
`plot`
`ppf`	The percent point function.
`rvs`	Random variable sampling.
`set_params`	Set the parameters of this model.
`sf`	The survival function.
`var`	The variance of the distribution.

cdf(time, ar, *args)[source]#

The cumulative density function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: cdf values at each given time(s).

chf(time, ar, *args)[source]#

The cumulative hazard function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: chf values at each given time(s).

freeze(ar, *args)[source]#

Freeze age replacement values and other arguments into the object data.

Parameters:

arfloat or np.ndarray: Age of replacement values. If ndarray, shape can only be (m,) as only one age of replacement per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

FrozenParametricModel

get_params()#

Get the parameters of this model.

Returns:

out1darray of number: Model parameters.

Notes

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

get_params_names()#

Parameters names.

Returns:

list of str: Parameters names

Notes

Parameters values can be requested (a.k.a. get) by their name at instance level.

hf(time, ar, *args)[source]#

The hazard function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: hf values at each given time(s).

ichf(cumulative_hazard_rate, ar, *args)[source]#

Inverse cumulative hazard function.

Parameters:

cumulative_hazard_ratefloat or np.ndarray: Cumulative hazard rate value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: ichf values at each given cumulative hazard rate(s).

isf(probability, ar, *args)[source]#

The inverse survival function.

Parameters:

probabilityfloat or np.ndarray: Probability value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: isf values at each given probability value(s).

ls_integrate(func, a, b, ar, *args, deg=10)[source]#

Lebesgue-Stieltjes integration.

Parameters:

funccallable (in1 ndarray , out1 ndarray): The callable must have only one ndarray object as argument and one ndarray object as output.
andarray (maximum number of dimension is 2): Lower bound(s) of integration.
bndarray (maximum number of dimension is 2): Upper bound(s) of integration. If lower bound(s) is infinite, use np.inf as value.
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.
degint, default 10: Degree of the polynomials interpolation.

Returns:

outnp.ndarray: Lebesgue-Stieltjes integral of func from a to b.

mean(ar, *args)[source]#

The mean of the distribution.

Parameters:

arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

median(ar, *args)[source]#

The median.

Parameters:

arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

moment(n, ar, *args)[source]#

n-th order moment.

Parameters:

nint: order of the moment, at least 1.
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64

mrl(time, ar, *args)[source]#

The mean residual life function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: Function values at each given time(s).

pdf(time, ar, *args)[source]#

The probability density function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: pdf values at each given time(s).

ppf(probability, ar, *args)[source]#

The percent point function.

Parameters:

probabilityfloat or np.ndarray: Probability value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: ppf values at each given probability value(s).

rvs(size, ar, *args, seed=None)[source]#

Random variable sampling.

Parameters:

sizeint or tuple (m, n) of int: Size of the generated sample.
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.
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: The sample values.

set_params(new_params)#

Set the parameters of this model.

Parameters:

new_paramsarray-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 be expressed in the static typesystem.

sf(time, ar, *args)[source]#

The survival function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n,) or (m, n).
arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray: sf values at each given time(s).

var(ar, *args)[source]#

The variance of the distribution.

Parameters:

arfloat or np.ndarray: Age of replacement values.

If ndarray, shape can only be (m,) because only one age of replacement per asset can be given.
*args: Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray