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class surpyval.univariate.parametric.parametric.Parametric(dist: Any, method: str, data: Any, offset: bool, lfp: bool, zi: bool)

Bases: ParametricDistribution

Result of .fit() or .from_params() method for every parametric surpyval distribution.

Instances of this class are very useful when a user needs the other functions of a distribution for plotting, optimizations, monte carlo analysis and numeric integration.

Hf(x: ArrayLike) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

The cumulative hazard function for a distribution using the parameters found in the .params attribute.

Parameters: x (array like or scalar) – The values of the random variables at which the cumulative hazard function will be calculated
Returns: Hf – The scalar value of the cumulative hazard function of the distribution if a scalar was passed. If an array like object was passed then a numpy array is returned with the value of the cumulative hazard function at each corresponding value in the input array.
Return type: scalar or numpy array

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.Hf(2)
0.008000000000000002
>>> model.Hf([1, 2, 3, 4, 5])
array([0.001, 0.008, 0.027, 0.064, 0.125])

aic() → float

The Aikake Information Criterion (AIC) for the model, if it was fit with the fit() method. Not available if fit with the from_params() method.

Returns: aic – The AIC of the model
Return type: float

Examples

>>> from surpyval import Weibull
>>> import numpy as np
>>> np.random.seed(1)
>>> x = Weibull.random(100, 10, 3)
>>> model = Weibull.fit(x)
>>> model.aic()
529.0537128477147

aic_c() → float

The Corrected Aikake Information Criterion (AIC) for the model, if it was fit with the fit() method. Not available if fit with the from_params() method.

Returns: aic_c – The Corrected AIC of the model
Return type: float

Examples

>>> from surpyval import Weibull
>>> import numpy as np
>>> np.random.seed(1)
>>> x = Weibull.random(100, 10, 3)
>>> model = Weibull.fit(x)
>>> model.aic()
529.1774241879209

bic() → float

The Bayesian Information Criterion (BIC) for the model, if it was fit with the fit() method. Not available if fit with the from_params() method.

Returns: bic – The BIC of the model
Return type: float

Examples

>>> from surpyval import Weibull
>>> import numpy as np
>>> np.random.seed(1)
>>> x = Weibull.random(100, 10, 3)
>>> model = Weibull.fit(x)
>>> model.bic()
534.2640532196908

References

Bayesian Information Criterion for Censored Survival Models.

cb(t: ArrayLike, on: str = 'sf', alpha_ci: float = 0.05, bound: str = 'two-sided') → ndarray[tuple[Any, ...], dtype[_ScalarT]]

Confidence bounds of the on function at the alpa_ci level of significance. Can be the upper, lower, or two-sided confidence by changing value of bound.

Parameters

x (array like or scalar) – The values of the random variables at which the confidence bounds will be calculated
on (('sf', 'ff', 'Hf', 'hf', 'df'), optional) – The function on which the confidence bound will be calculated.
bound (('two-sided', 'upper', 'lower'), str, optional) – Compute either the two-sided, upper or lower confidence bound(s). Defaults to two-sided.
alpha_ci (scalar, optional) – The level of significance at which the bound will be computed.

Returns

cb – The value(s) of the upper, lower, or both confidence bound(s) of the selected function at x

Return type

scalar or numpy array

cs(x: ArrayLike, X: ArrayLike) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

The conditional survival of the model; that is, the probability that an item that has survived to X survives a further x:

\[R(x, X) = \frac{R(x + X)}{R(X)}\]

Parameters

x (array like or scalar) – The further durations at which conditional survival is to be calculated.
X (array like or scalar) – The value(s) at which it is known the item has survived

Returns

cs – The conditional survival probability.

Return type

array

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.cs(11, 10)
0.00025840046151723767

df(x: ArrayLike) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

The density function for a distribution using the parameters found in the .params attribute.

Parameters: x (array like or scalar) – The values of the random variables at which the density function will be calculated.
Returns: df – The scalar value of the density function of the distribution if a scalar was passed. If an array like object was passed then a numpy array is returned with the value of the density function at each corresponding value in the input array.
Return type: scalar or numpy array

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.df(2)
0.01190438297804473
>>> model.df([1, 2, 3, 4, 5])
array([0.002997  , 0.01190438, 0.02628075, 0.04502424, 0.06618727])

entropy() → float

The entropy of the distribution using the parameters found in the .params attribute.

Returns: entropy – Returns entropy of the distribution
Return type: float

Examples

>>> from surpyval import Normal
>>> model = Normal.from_params([10, 3])
>>> model.entropy()
2.5175508218727822

ff(x: ArrayLike) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

The cumulative distribution function, or failure function, for a distribution using the parameters found in the .params attribute.

Parameters: x (array like or scalar) – The values of the random variables at which the failure function (CDF) will be calculated.
Returns: ff – The scalar value of the CDF of the distribution if a scalar was passed. If an array like object was passed then a numpy array is returned with the value of the CDF at each corresponding value in the input array.
Return type: scalar or numpy array

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.ff(2)
0.007968085162939342
>>> model.ff([1, 2, 3, 4, 5])
array([0.0009995 , 0.00796809, 0.02663876, 0.061995  , 0.1175031 ])

get_plot_data(heuristic: str = 'Nelson-Aalen', alpha_ci: float = 0.05) → dict

A method to gather plot data

Parameters

heuristic ({'Blom', 'Median', 'ECDF', 'Modal', 'Midpoint', 'Mean', 'Weibull', 'Benard', 'Beard', 'Hazen', 'Gringorten', 'None', 'Tukey', 'DPW', 'Fleming-Harrington', 'Kaplan-Meier', 'Nelson-Aalen', 'Filliben', 'Larsen', 'Turnbull'}, optional) – The method that the plotting point on the probability plot will be calculated. Default is “Nelson-Aalen”.
alpha_ci (float, optional) – The level of significance at which the confidence bounds, if able, will be calculated. Defaults to 0.05.

Returns

data – Returns dictionary containing the data needed to do a plot.

Return type

dict

Examples

>>> from surpyval import Weibull
>>> x = Weibull.random(100, 10, 3)
>>> model = Weibull.fit(x)
>>> data = model.get_plot_data()

hf(x: ArrayLike) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

The instantaneous hazard function for a distribution using the parameters found in the .params attribute.

Parameters: x (array like or scalar) – The values of the random variables at which the instantaneous hazard function will be calculated.
Returns: hf – The scalar value of the instantaneous hazard function of the distribution if a scalar was passed. If an array like object was passed then a numpy array is returned with the value of the instantaneous hazard function at each corresponding value in the input array.
Return type: scalar or numpy array

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.hf(2)
0.012000000000000002
>>> model.hf([1, 2, 3, 4, 5])
array([0.003, 0.012, 0.027, 0.048, 0.075])

mean() → float

The mean of the distribution using the parameters found in the .params attribute.

Returns: mean – Returns the mean of the distribution.
Return type: float

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.mean()
8.929795115692489

moment(n: int) → float

The n-th moment of the distribution using the parameters found in the .params attribute.

Parameters: n (integer) – The degree of the moment to be computed
Returns: moment[n] – Returns the n-th moment of the distribution
Return type: float

Examples

>>> from surpyval import Normal
>>> model = Normal.from_params([10, 3])
>>> model.moment(1)
10.0
>>> model.moment(5)
202150.0

neg_ll() → float

The negative log-likelihood for the model, if it was fit with the fit() method. Not available if fit with the from_params() method.

Returns: neg_ll – The negative log-likelihood of the model
Return type: float

Examples

>>> from surpyval import Weibull
>>> import numpy as np
>>> np.random.seed(1)
>>> x = Weibull.random(100, 10, 3)
>>> model = Weibull.fit(x)
>>> model.neg_ll()
262.52685642385734

param_cb(name: str, alpha_ci: float = 0.05, bound: str = 'two-sided') → ndarray[tuple[Any, ...], dtype[_ScalarT]]: Method to calculate the confidence bound on a parameter.

plot(heuristic: str = 'Nelson-Aalen', plot_bounds: bool = True, alpha_ci: float = 0.05, ax: Axes | None = None) → list

A method to do a probability plot

Parameters

heuristic ({'Blom', 'Median', 'ECDF', 'Modal', 'Midpoint', 'Mean', 'Weibull', 'Benard', 'Beard', 'Hazen', 'Gringorten', 'None', 'Tukey', 'DPW', 'Fleming-Harrington', 'Kaplan-Meier', 'Nelson-Aalen', 'Filliben', 'Larsen', 'Turnbull'}, optional) – The method that the plotting point on the probability plot will be calculated.
plot_bounds (Boolean, optional) – A Boolean value to indicate whether you want the probability bounds to be calculated.
alpha_ci (float, optional) – The level of significance at which the confidence bounds, if able, will be calculated. Defaults to 0.05.
ax (matplotlib.axes.Axes, optional) – The axis onto which the plot will be created. Optional, if not provided a new axes will be created.

Returns

plot – list of a matplotlib plot object

Return type

list

Examples

>>> from surpyval import Weibull
>>> x = Weibull.random(100, 10, 3)
>>> model = Weibull.fit(x)
>>> model.plot()

qf(p: ArrayLike) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

The quantile function for a distribution using the parameters found in the .params attribute.

Parameters: p (array like or scalar) – The values, which must be between 0 and 1, at which the the quantile will be calculated
Returns: qf – The scalar value of the quantile of the distribution if a scalar was passed. If an array like object was passed then a numpy array is returned with the value of the quantile at each corresponding value in the input array.
Return type: scalar or numpy array

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.qf(0.2)
6.06542793124108
>>> model.qf([.1, .2, .3, .4, .5])
array([4.72308719, 6.06542793, 7.09181722, 7.99387877, 8.84997045])

random(size: int | tuple[int, ...], a: float | None = None, b: float | None = None) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

A method to draw random samples from the distributions using the parameters found in the .params attribute.

Parameters

size (int) – The number of random samples to be drawn from the distribution.
a (float or None) – The left truncated value if sampling from a truncated distribution
b (float or None) – The right truncated value if sampling from a truncated distribution

Returns

random – Returns a numpy array of size size with random values drawn from the distribution.

Return type

numpy array

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> np.random.seed(1)
>>> model.random(1)
array([8.14127103])
>>> model.random(10)
array([10.84103403,  0.48542084,  7.11387062,  5.41420125, 4.59286657,
        5.90703589,  7.5124326 ,  7.96575225,  9.18134126, 8.16000438])

sf(x: ArrayLike) → ndarray[tuple[Any, ...], dtype[_ScalarT]]

Survival (or Reliability) function for a distribution using the parameters found in the .params attribute.

Parameters: x (array like or scalar) – The values of the random variables at which the survival function will be calculated.
Returns: sf – The scalar value of the survival function of the distribution if a scalar was passed. If an array like object was passed then a numpy array is returned with the value of the survival function at each corresponding value in the input array.
Return type: scalar or numpy array

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.sf(2)
0.9920319148370607
>>> model.sf([1, 2, 3, 4, 5])
array([0.9990005 , 0.99203191, 0.97336124, 0.938005  , 0.8824969 ])

var() → float

The variance of the distribution using the parameters found in the .params attribute.

Returns: var – Returns the variance of the distribution.
Return type: float

Examples

>>> from surpyval import Weibull
>>> model = Weibull.from_params([10, 3])
>>> model.var()
11.229...