Probability Group
Contents
Probability Group of functions defined on Loss and Gain includes the following functions:
Full Name |
Brief Name |
Short Description |
pr_pen |
Probability that Linear Loss exceeds some fixed threshold. |
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pr_pen_g |
Probability that Linear -(Loss ) exceeds some fixed threshold. |
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pr_pen_ni |
Probability that Linear Loss exceeds some fixed threshold for the Loss with independent normally distributed random coefficients. |
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pr_pen_ni_g |
Probability that Linear -(Loss ) exceeds some fixed threshold for the Loss with independent normally distributed random coefficients. |
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pr_pen_nd |
Probability that Linear Loss exceeds some fixed threshold for the Loss with mutually dependent normally distributed random coefficients. |
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pr_pen_nd_g |
Probability that Linear -(Loss ) exceeds some fixed threshold for the Loss with mutually dependent normally distributed random coefficients |
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pr_dev |
Probability that (Loss)-(Average Loss) exceeds some fixed threshold. |
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pr_dev_g |
Probability that -(Loss)+(Average Loss) exceeds some fixed threshold. |
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pr_ni_dev |
Probability that (Loss)-(Average Loss) exceeds some fixed threshold for the Loss with independent normally distributed random coefficients. |
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Probability of Exceedance Deviation for Gain Normal Independent |
pr_ni_dev_g |
Probability that -(Loss)+(Average Loss) exceeds some fixed threshold for the Loss with independent normally distributed random coefficients. |
pr_nd_dev |
Probability that (Loss)-(Average Loss) exceeds some fixed threshold for the Loss with mutually dependent normally distributed random coefficients |
|
Probability of Exceedance Deviation for Gain Normal Dependent |
pr_nd_dev_g |
Probability that -(Loss)+(Average Loss) exceeds some fixed threshold for the Loss with mutually dependent normally distributed random coefficients |
avg_pr_pen_ni |
Consider a mixture of (random) Linear Loss functions with positive weights summing up to one. Coefficients in all Linear Loss functions are independent normally distributed random values. Average Probability of Exceedance Normal Independent is a weighted sum of Probability of Exceedance Normal functions over all Loss functions in the mixture. The weighs in the sum are taken from the mixture of Loss functions. |
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Average Probability of Exceedance for Gain Normal Independent |
avg_pr_pen_ni_g |
Consider a mixture of (random) Linear Loss functions with positive weights summing up to one. Coefficients in all Linear Loss functions are independent normally distributed random values. Average Probability of Exceedance for Gain Normal Independent is a weighted sum of Probability of Exceedance for Gain Normal Independent functions over all Loss functions in the mixture. The weighs in the sum are taken from the mixture of Loss functions. |
Average Probability of Exceedance Deviation Normal Independent |
avg_pr_ni_dev |
Consider a mixture of (random) Linear Loss functions with positive weights summing up to one. Coefficients in all Linear Loss functions are independent normally distributed random values. Average Probability of Exceedance Deviation Normal Independent is a weighted sum of Probability of Exceedance Deviation Normal Independent functions over all Loss functions in the mixture. The weighs in the sum are taken from the mixture of Loss functions. |
prmulti_pen |
There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Loss scenarios function is calculated by maximizing losses over Linear Loss functions (over M functions for every scenario). Probability of Exceedance Multiple is the Probability of Exceedance of the Maximum Loss scenarios. (Probability of Exceedance Multiple) = 1-(Probability that all M Linear Loss functions are below the threshold). |
|
prmulti_pen_g |
There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum -Loss scenarios function is calculated by maximizing losses over -Loss functions (over M functions for every scenario). Probability of Exceedance for Gain Multiple is Probability of Exceedance of the Maximum -Loss scenarios. (Probability of Exceedance for Gain Multiple) = 1-(Probability that all M Linear -(Loss) functions are below the threshold). |
|
prmulti_pen_ni |
There are M Linear Loss scenario functions with independent normally distributed random coefficients. Probability of Exceedance Multiple Normal Independent = 1-(Probability that all M Linear Loss functions are below the threshold). |
|
Probability of Exceedance for Gain Multiple Normal Independent |
prmulti_pen_ni_g |
There are M Linear Loss scenario functions with independent normally distributed random coefficients. Probability of Exceedance for Gain Multiple Normal Independent = 1-(Probability that all M -(Loss) functions are below the threshold). |
prmulti_pen_nd |
There are M Linear Loss scenario functions with mutually dependent normally distributed random coefficients. Probability of Exceedance Multiple Normal Dependent = 1-(Probability that all M Linear Loss functions are below the threshold). |
|
Probability of Exceedance for Gain Multiple Normal Dependent |
prmulti_pen_nd_g |
There are M Linear Loss scenario functions with mutually dependent normally distributed random coefficients. Probability of Exceedance for Gain Multiple Normal Dependent = 1-(Probability that all M -(Loss) functions are below the threshold). |
prmulti_dev |
There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Deviation Multiple scenarios function is calculated by maximizing losses over (Loss)-(Average Loss) functions (over M functions for every scenario). Probability of Exceedance Deviation Multiple is the Probability of Exceedance of the Maximum Maximum Deviation Multiple scenarios. (Probability of Exceedance Deviaiont Multiple) = 1-(Probability that all M (Loss)-(Average Loss) functions are below the threshold). |
|
prmulti_dev_g |
There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Deviation for Gain Multiple scenarios function is calculated by maximizing losses over -(Loss)+(Average Loss) functions (over M functions for every scenario). Probability of Exceedance Deviation for Gain Multiple is the Probability of Exceedance of the Maximum Maximum Deviation for Gain Multiple scenarios. (Probability of Exceedance Penalty for Gain Multiple) = 1-(Probability that all M -(Loss)+(Average Loss) functions are below the threshold). |
|
Probability of Exceedance Deviation Multiple Normal Independent |
prmulti_ni_dev |
There are M Linear Loss scenario functions with independent normally distributed random coefficients. Probability of Exceedance Deviation Multiple Normal Independent = 1-(Probability that all M (Loss)-(Average Loss) functions are below the threshold). |
Probability of Exceedance Deviation Multiple Normal Dependent |
prmulti_nd_dev |
There are M Linear Loss scenario functions with mutually dependent normally distributed random coefficients. Probability of Exceedance Deviation Multiple Normal Dependent = 1-(Probability that all M (Loss)-(Average Loss) functions are below the threshold). |
bpoe |
(1-confidence_level) of CVaR for Linear Loss if threshold less than average loss and (1-confidence_level) of CVaR of gains otherwise. |
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pr_pen(recourse(.)) |
Probability that Recourse scenarios function exceeds some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario. |
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pr_pen_g(recourse(.)) |
Probability that -(Recourse) scenarios function exceeds some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario. |
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pr_dev(recourse(.)) |
Probability that (Recourse)-(Average Recourse) scenarios function exceeds some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario. |
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pr_dev_g(recourse(.)) |
Probability that -(Recourse)+(Average Recourse) scenarios function exceeds some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario. |
Remarks
| 1. | Threshold w may be any real number. |
| 2. | Functions from the Probability group are calculated with double precision. |
| 3. | Any function from this group may be called by its "brief name" or by "brief name" with "optional name" |
| • | The optional name of any function from this group may contain up to 128 symbols. |
| • | Optional names of these functions may include only alphabetic characters, numbers, and the underscore sign, "_". |
| • | Optional names of these functions are "insensitive" to the case, i.e. there is no difference between low case and upper case in these names. |