bounds_surv_probability

rearrangement_algorithm.bounds_surv_probability(quant, s_level: float, num_steps: int = 10, abstol: float = 0, lookback: int = 0, max_ra: int = 0, cost_func=<function sum>, method: str = 'lower', sample: bool = True)

Computing the lower/upper bounds on the survival probability of a function of dependent risks

This function performs the RA and calculates the lower and upper bounds on the survival probability of function of dependent random variables. For mathematical details, see 1.

Parameters

  • quant (list) – List of marginal quantile functions

  • s_level (float) – Value of the function of the random variables at which the survival probability bounds are calculated.

  • num_steps (int) – Number of discretization points

  • abstol (float) – Absolute convergence tolerance

  • lookback (int) – Number of column rearrangements to look back for deciding about convergence. Must be a number in \(\{1, ..., \text{max_ra}-1\}\). If set to zero, it defaults to len(quant).

  • max_ra (int) – Number of column rearrangements. If zero, it defaults to infinitely many.

  • cost_func (callable) – Callable function that represent the function which is applied to the dependent random variables. It needs to accept the axis=1 keyword argument and handle it in the numpy style, i.e., taking a 2D-array as input and returning a column-vector.

  • method (str) –

    Determine if the lower or upper bound on the expected value is computed. Valid options are:

    • lower: for the lower bound

    • upper: for the upper bound

  • sample (bool) – Indication whether each column of the two working matrices is randomly permuted before the rearrangements begin

Returns

  • bound_low (float) – Lower bound on the survival probability

  • x_ra_low (numpy.array) – Rearranged matrix for the lower bound

  • bound_up (float) – Upper bound on the survival probability

  • x_ra_up (numpy.array) – Rearranged matrix for the upper bound

References

1

G. Puccetti and L. Rüschendorf, “Computation of sharp bounds on the distribution of a function of dependent risks,” Journal of Computational and Applied Mathematics, vol. 236, no. 7, pp. 1833-1840, Jan. 2012.