Beta_Distribution¶

class
reliability.Distributions.
Beta_Distribution
(alpha=None, beta=None, **kwargs)¶ Beta probability distribution
Creates a Distribution object in the range 01.
Inputs: alpha  shape parameter 1 beta  shape parameter 2
Methods: name  ‘Beta’ name2  ‘Beta_2P’ param_title_long  Useful in plot titles, legends and in printing strings. eg. ‘Beta Distribution (α=5,β=2)’ param_title  Useful in plot titles, legends and in printing strings. eg. ‘α=5,β=2’ parameters  [alpha,beta] alpha beta mean variance standard_deviation skewness kurtosis excess_kurtosis median mode b5 b95 plot()  plots all functions (PDF,CDF,SF,HF,CHF) PDF()  plots the probability density function CDF()  plots the cumulative distribution function SF()  plots the survival function (also known as reliability function) HF()  plots the hazard function CHF()  plots the cumulative hazard function quantile()  Calculates the quantile (time until a fraction has failed) for a given fraction failing.
Also known as b life where b5 is the time at which 5% have failed.inverse_SF()  the inverse of the Survival Function. This is useful when producing QQ plots. mean_residual_life()  Average residual lifetime of an item given that the item has survived up to a given time.
Effectively the mean of the remaining amount (right side) of a distribution at a given time.stats()  prints all the descriptive statistics. Same as the statistics shown using .plot() but printed to console. random_samples()  draws random samples from the distribution to which it is applied. Same as rvs in scipy.stats.

CDF
(xvals=None, xmin=None, xmax=None, show_plot=True, **kwargs)¶ Plots the CDF (cumulative distribution function)
Inputs: show_plot  True/False. Default is True xvals  xvalues for plotting xmin  minimum xvalue for plotting xmax  maximum xvalue for plotting *If xvals is specified, it will be used. If xvals is not specified but xmin and xmax are specified then an array with 200 elements will be created using these ranges. If nothing is specified then the range will be based on the distribution’s parameters. *plotting keywords are also accepted (eg. color, linestyle)
Outputs: yvals  this is the yvalues of the plot The plot will be shown if show_plot is True (which it is by default).

CHF
(xvals=None, xmin=None, xmax=None, show_plot=True, **kwargs)¶ Plots the CHF (cumulative hazard function)
Inputs: show_plot  True/False. Default is True xvals  xvalues for plotting xmin  minimum xvalue for plotting xmax  maximum xvalue for plotting *If xvals is specified, it will be used. If xvals is not specified but xmin and xmax are specified then an array with 200 elements will be created using these ranges. If nothing is specified then the range will be based on the distribution’s parameters. *plotting keywords are also accepted (eg. color, linestyle)
Outputs: yvals  this is the yvalues of the plot The plot will be shown if show_plot is True (which it is by default).

HF
(xvals=None, xmin=None, xmax=None, show_plot=True, **kwargs)¶ Plots the HF (hazard function)
Inputs: show_plot  True/False. Default is True xvals  xvalues for plotting xmin  minimum xvalue for plotting xmax  maximum xvalue for plotting *If xvals is specified, it will be used. If xvals is not specified but xmin and xmax are specified then an array with 200 elements will be created using these ranges. If nothing is specified then the range will be based on the distribution’s parameters. *plotting keywords are also accepted (eg. color, linestyle)
Outputs: yvals  this is the yvalues of the plot The plot will be shown if show_plot is True (which it is by default).

PDF
(xvals=None, xmin=None, xmax=None, show_plot=True, **kwargs)¶ Plots the PDF (probability density function)
Inputs: show_plot  True/False. Default is True xvals  xvalues for plotting xmin  minimum xvalue for plotting xmax  maximum xvalue for plotting *If xvals is specified, it will be used. If xvals is not specified but xmin and xmax are specified then an array with 200 elements will be created using these ranges. If nothing is specified then the range will be based on the distribution’s parameters. *plotting keywords are also accepted (eg. color, linestyle)
Outputs: yvals  this is the yvalues of the plot The plot will be shown if show_plot is True (which it is by default).

SF
(xvals=None, xmin=None, xmax=None, show_plot=True, **kwargs)¶ Plots the SF (survival function)
Inputs: show_plot  True/False. Default is True xvals  xvalues for plotting xmin  minimum xvalue for plotting xmax  maximum xvalue for plotting *If xvals is specified, it will be used. If xvals is not specified but xmin and xmax are specified then an array with 200 elements will be created using these ranges. If nothing is specified then the range will be based on the distribution’s parameters. *plotting keywords are also accepted (eg. color, linestyle)
Outputs: yvals  this is the yvalues of the plot The plot will be shown if show_plot is True (which it is by default).

inverse_SF
(q)¶ Inverse Survival function calculator
Parameters: q – quantile to be calculated Returns: the inverse of the survival function at q

mean_residual_life
(t)¶ Mean Residual Life calculator
Parameters: t – time at which MRL is to be evaluated Returns: MRL

plot
(xvals=None, xmin=None, xmax=None)¶ Plots all functions (PDF, CDF, SF, HF, CHF) and descriptive statistics in a single figure
Inputs: xvals  xvalues for plotting xmin  minimum xvalue for plotting xmax  maximum xvalue for plotting *If xvals is specified, it will be used. If xvals is not specified but xmin and xmax are specified then an array with 200 elements will be created using these ranges. If nothing is specified then the range will be based on the distribution’s parameters. *no plotting keywords are accepted
Outputs: The plot will be shown. No need to use plt.show()

quantile
(q)¶ Quantile calculator
Parameters: q – quantile to be calculated Returns: the probability (area under the curve) that a random variable from the distribution is < q

random_samples
(number_of_samples, seed=None)¶ Draws random samples from the probability distribution
Parameters:  number_of_samples – the number of samples to be drawn
 seed – the random seed. Default is None
Returns: the random samples

stats
()¶ Descriptive statistics of the probability distribution. Same as the statistics shown using .plot() but printed to console. No inputs or outputs.
