LogLogistic#

final class relife.lifetime_model.LogLogistic(shape=None, rate=None)[source]#

Log-logistic probability distribution.

The Log-logistic distribution is defined as a 2-parameter distribution \((c, \lambda)\). The probability density function is:

\[f(t) = \frac{c \lambda^c t^{c-1}}{(1+(\lambda t)^{c})^2}\]

where:

\(c > 0\), the shape parameter,

\(\lambda > 0\), the rate parameter,

\(t\geq 0\), the operating time, age, cycles, etc.

Parameters:

shapefloat, default is None: Shape parameter.
ratefloat, default is None: Rate parameter.

Attributes:

fitting_resultsFittingResults, default is None: An object containing fitting results (AIC, BIC, etc.). If the model is not fitted, the value is None.
nb_params: Number of parameters.
params: Parameters values.
params_names: Parameters names.
plot: Provides access to plotting functionnalities
shape: Returns the shape value.
rate: Returns the rate value.

Methods

`cdf`	The cumulative density function.
`chf`	The cumulative hazard function.
`dhf`	The derivate of the hazard function.
`fit`	Estimation of the distribution parameters from lifetime data.
`fit_from_interval_censored_lifetimes`	Estimation of the distribution parameters from interval censored lifetime data.
`get_initial_params`	Gets the inital parameters values used in before fitting.
`hf`	The hazard function.
`ichf`	Inverse cumulative hazard function.
`isf`	The inverse survival function.
`jac_cdf`	The jacobian of the cumulative density function.
`jac_chf`	The jacobian of the cumulative hazard function.
`jac_hf`	The jacobian of the hazard function.
`jac_pdf`	The jacobian of the probability density function.
`jac_sf`	The jacobian of the 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)#

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).

Returns:

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

chf(time)[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).

Returns:

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

dhf(time)[source]#

The derivate of 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).

Returns:

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

fit(time, model_args=None, event=None, entry=None, optimizer_options=None)#

Estimation of the distribution parameters from lifetime data.

Parameters:

time1d array

Observed lifetime values.

model_argsany ndarray or tuple of ndarray, default is None

Any additional arguments required by the model.

event1d array of bool, default is None

Boolean indicators tagging lifetime values as right censored or complete.

entry1d array, default is None

Left truncations applied to lifetime values.

optimizer_optionsdict, default is None

Extra arguments used by scipy.minimize. Default values are:

method : “L-BFGS-B”
contraints : ()
tol : None
callback : None
options : None
bounds : self.params_bounds
x0 : self.init_params

Returns:

outthe object instance: The estimated parameters are setted inplace.

fit_from_interval_censored_lifetimes(time_inf, time_sup, model_args=None, entry=None, optimizer_options=None)#

Estimation of the distribution parameters from interval censored lifetime data.

Parameters:

time_inf1d array

Observed lifetime lower bounds.

time_sup1d array

Observed lifetime upper bounds.

model_argsany ndarray or tuple of ndarray, default is None

Any additional arguments required by the model.

entry1d array, default is None

Left truncations applied to lifetime values.

optimizer_optionsdict, default is None

Extra arguments used by scipy.minimize. Default values are:

method : “L-BFGS-B”
contraints : ()
tol : None
callback : None
options : None
bounds : self.params_bounds
x0 : self.init_params

Returns:

outthe object instance: The estimated parameters are setted inplace.

Notes

Where time_inf == time_sup, lifetimes are complete.

get_initial_params(time, event=None, model_args=None)#

Gets the inital parameters values used in before fitting.

Parameters:

time1d array: Observed lifetime values.
event1d array of bool, default is None: Boolean indicators tagging lifetime values as right censored or complete. If it is not None, it will be used to select only complete lifetimes.
model_argsany ndarray or tuple of ndarray, default is None: Any additional arguments required by the model.

Returns:

out1d array of float

hf(time)[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).

Returns:

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

ichf(cumulative_hazard_rate)[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).

Returns:

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

isf(probability)#

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).

Returns:

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

jac_cdf(time)#

The jacobian of 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).

Returns:

outnp.float64 or np.ndarray: The derivatives with respect to each parameter. If the result is an np.ndarray, the first dimension holds the number of parameters.

jac_chf(time)[source]#

The jacobian of 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).

Returns:

outnp.float64 or np.ndarray: The derivatives with respect to each parameter. If the result is an np.ndarray, the first dimension holds the number of parameters.

jac_hf(time)[source]#

The jacobian of 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).

Returns:

outnp.float64 or np.ndarray: The derivatives with respect to each parameter. If the result is an np.ndarray, the first dimension holds the number of parameters.

jac_pdf(time)#

The jacobian of 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).

Returns:

outnp.float64 or np.ndarray: The derivatives with respect to each parameter. If the result is an np.ndarray, the first dimension holds the number of parameters.

jac_sf(time)#

The jacobian of 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).

Returns:

outnp.float64 or np.ndarray: The derivatives with respect to each parameter. If the result is an np.ndarray, the first dimension holds the number of parameters.

ls_integrate(func, a, b, *, 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.
degint, default 10: Degree of the polynomials interpolation.

Returns:

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

mean()[source]#

The mean of the distribution.

Returns:

outnp.float64

median()#

The median.

Returns:

outnp.float64

moment(n)#

n-th order moment.

Parameters:

nint: order of the moment, at least 1.

Returns:

outnp.float64

mrl(time)[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).

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_bounds#: Parameters bounds

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)#

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).

Returns:

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

property plot#: Provides access to plotting functionnalities

ppf(probability)#

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).

Returns:

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

property rate#

Returns the rate value.

Returns:

out: float

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

Random variable sampling.

Parameters:

sizeint or tuple (m, n) of int: Size of the generated sample.
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)#

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).

Returns:

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

property shape#

Returns the shape value.

Returns:

out: float

var()[source]#

The variance of the distribution.

Returns:

outnp.float64

LogLogistic#

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