LeftTruncatedModel#

class relife.lifetime_model.LeftTruncatedModel(baseline)#

Left truncated model.

Lifetime model where the assets have already reached the age \(a_0\).

Parameters:

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

Methods

`cdf`	The cumulative distribution function.
`chf`	The cumulative hazard function.
`hf`	The hazard function.
`ichf`	Inverse cumulative hazard function.
`isf`	Inverse survival function.
`ls_integrate`	Lebesgue-Stieltjes integration.
`mean`	The mean.
`median`	The median.
`moment`	n-th order moment
`mrl`	The mean residual life function.
`pdf`	The probability density function.
`ppf`	The percent point function.
`rvs`	Random variable sampling.
`sf`	The survival function.
`var`	The variance.

cdf(time, ar, *args)#

The cumulative distribution function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n_values,) or (n_assets, n_values).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

chf(time, a0, *args)#

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_values,) or (n_assets, n_values).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

hf(time, a0, *args)#

The hazard function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n_values,) or (n_assets, n_values).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

ichf(cumulative_hazard_rate, a0, *args)#

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).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

isf(probability, a0, *args)#

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).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

ls_integrate(func, a, b, a0, *args, deg=10)#

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.)
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.
degint, default 10: Degree of the polynomials interpolation

Returns:

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

mean(a0, *args)#

The mean.

Parameters:

a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

np.float64: The mean value.

median(a0, *args)#

The median.

Parameters:

a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

np.float64: The median value.

moment(n, a0, *args)#

n-th order moment

Parameters:

norder of the moment, at least 1.

Returns:

np.float64: n-th order moment.

mrl(time, a0, *args)#

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_values,) or (n_assets, n_values).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

property nb_params#

Number of parameters.

Returns:

int: Number of parameters.

property params#

Parameters values.

Returns:

ndarray: Parameters values of the core

Notes

If parameter values are not set, they are encoded as np.nan value.

Parameters can be by manually setting`params` through its setter, fitting the core if fit exists or by specifying all parameters values when the core object is initialized.

property 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.

pdf(time, a0, *args)#

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_values,) or (n_assets, n_values).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

property plot#: Provides access to plotting functionality for this distribution.

ppf(probability, a0, *args)#

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).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

Notes

The ppf is the inverse of cdf().

rvs(size, a0, *args, return_event=False, return_entry=False, seed=None)#

Random variable sampling.

Parameters:

sizeint, (int,) or (int, int): Size of the generated sample. If size is n or (n,), n samples are generated. If size is (m,n), a 2d array of samples is generated.
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.
return_eventbool, default is False: If True, returns event indicators along with the sample time values.
return_entrybool, default is False: If True, returns corresponding entry values of the sample time values.
seedoptional int, default is None: Random seed used to fix random sampling.

Returns:

float, ndarray or tuple of float or ndarray: The sample values. If either return_event or random_entry is True, returns a tuple containing the time values followed by event values, entry values or both.

sf(time, a0, *args)#

The survival function.

Parameters:

timefloat or np.ndarray: Elapsed time value(s) at which to compute the function. If ndarray, allowed shapes are (), (n_values,) or (n_assets, n_values).
a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

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

var(a0, *args)#

The variance.

Parameters:

a0float or np.ndarray: Conditional age values. It represents ages reached by assets. If ndarray, shape can only be (m,) as only one age per asset can be given
*argsfloat or np.ndarray: Additional arguments needed by the model.

Returns:

np.float64: The variance value.

LeftTruncatedModel#

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