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

nb_params

params

params_names

plot

Attributes:

baseline

nb_params

Number of parameters.

params

Parameters values.

params_names

Parameters names.

plot

Provides access to plotting functionnalities

Methods

cdf	The cumulative density function.
chf	The cumulative hazard function.
freeze	Freeze conditional age values and other arguments into the object data.
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.
ppf	The percent point function.
rvs	Random variable sampling.
sf	The survival function.
var	The variance of the distribution.

cdf(time, a0, *args)

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).

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

cdf 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,) or (m, n).

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

chf values at each given time(s).

freeze(a0, *args)

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

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:

FrozenLeftTruncatedModel

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,) or (m, n).

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*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, 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

Current ages. If ndarray, shape can only be (m,).

*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, a0, *args)

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).

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*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, 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

Current ages. If ndarray, shape can only be (m,).

*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(a0, *args)

The mean of the distribution.

Parameters:

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

median(a0, *args)

The median.

Parameters:

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

moment(n, a0, *args)

n-th order moment.

Parameters:

nint

order of the moment, at least 1.

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64

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,) or (m, n).

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.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

Notes

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

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,) or (m, n).

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

pdf values at each given time(s).

property plot

Provides access to plotting functionnalities

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

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

ppf values at each given probability value(s).

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

Random variable sampling.

Parameters:

sizeint or tuple (m, n) of int

Size of the generated sample.

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other 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, 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, ndarray or tuple of float or ndarray

The sample values. If either return_event or return_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,) or (m, n).

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray

sf values at each given time(s).

var(a0, *args)

The variance of the distribution.

Parameters:

a0float or np.ndarray

Current ages. If ndarray, shape can only be (m,).

*args

Any other arguments needed by the model.

Returns:

outnp.float64 or np.ndarray