Partial Moment Group

Full Name

Brief Name

Short Description

Partial Moment

pm_pen

Expected  access of  Linear Loss over some fixed threshold.

Partial Moment for Gain

pm_pen_g

Expected  access of  -( Loss ) over some fixed threshold.

Partial Moment Normal Independent

pm_pen_ni

Expected  access of  Linear Loss over some fixed threshold  for the Loss with independent normally distributed random coefficients.

Partial Moment for Gain Normal Independent

pm_pen_ni_g

Expected  access of  - (Loss ) over some fixed threshold  for the Loss with independent normally distributed random coefficients.

Partial Moment Normal Dependent

pm_pen_nd

Expected  access of Loss over some fixed threshold  for the Loss with mutually dependent normally distributed random coefficients.

Partial Moment for Gain Normal Dependent

pm_pen_nd_g

Expected  access of  - (Loss ) over some fixed threshold  for the Loss with mutually dependent normally distributed random coefficients.

Partial Moment  Deviation

pm_dev

Expected  access of  ( (Loss ) - (Average Loss )) over some fixed threshold.

Partial Moment Gain Deviation

pm_dev_g

Expected  access of  (- (Loss ) + (Average Loss )) over some fixed threshold.

Partial Moment  Deviation Normal Independent

pm_ni_dev

Expected  access of  ( (Loss ) - (Average Loss )) over some fixed threshold for the Loss with independent normally distributed random coefficients.

Partial Moment Gain Deviation Normal Independent

pm_ni_dev_g

Expected  access of  ( - (Loss ) + (Average Loss )) over some fixed threshold for the Loss with independent normally distributed random coefficients.

Partial Moment  Deviation Normal Dependent

pm_nd_dev

Expected  access of ( (Loss ) - (Average Loss ))  over some fixed threshold for the Loss with mutually dependent normally distributed random coefficients.

Partial Moment Gain Deviation Normal Dependent

pm_nd_dev_g

Expected  access of   (- (Loss ) + (Average Loss ))  over some fixed threshold for the Loss with mutually dependent normally distributed random coefficients.

Average Partial Moment  Normal Independent

avg_pm_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 Partial Moment Normal Independent is a weighted sum of Partial Moment  Normal Independent functions over all Loss functions in the mixture. The weighs in the sum are taken from the mixture of Loss functions.

Average Partial Moment  for Gain Normal Independent

avg_pm_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 Partial Moment for Gain Normal Independent is a weighted sum of Partial Moment 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 Partial Moment Deviation Normal Independent

avg_pm_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 Partial Moment Deviation Normal Independent is a weighted sum of Partial Moment  Deviation Normal Independent functions over all Loss functions in the mixture. The weighs in the sum are taken from the mixture of Loss functions.

Average Partial Moment Gain Deviation Normal Independent

avg_pm_ni_dev_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 Partial Moment Gain Deviation Normal Independent is a weighted sum of Partial Moment Gain Deviation Normal Dependent functions over all Loss functions in the mixture. The weighs in the sum are taken from the mixture of Loss functions.

Partial Moment Two

pm2_pen

Expected  squared Linear Loss in access of of some fixed threshold.

Partial Moment Twofor Gain

pm2_pen_g

Expected  squared Linear -(Loss ) in access of of some fixed threshold.

Partial Moment Two  Normal Independent

pm2_pen_ni

Expected  squared Linear Loss in access of of some fixed threshold for Loss with independent normally distributed random coefficients.

Partial Moment Two for Gain Normal Independent

pm2_pen_ni_g

Expected  squared Linear -(Loss)  in access of of some fixed threshold for Loss with independent normally distributed random coefficients.

Partial Moment Two Normal Dependent

pm2_pen_nd

Expected  squared Linear Loss in access of of some fixed threshold for the Loss with mutually dependent normally distributed random coefficients.

Partial Moment Two for Gain Normal Dependent

pm2_pen_nd_g

Expected  squared Linear -(Loss ) in access of of some fixed threshold for the Loss with mutually dependent normally distributed random coefficients.

Partial Moment Two Deviation for Loss

pm2_dev

Expected  squared access of  ((Loss ) - (Average Loss )) over some fixed threshold.

Partial Moment Two Deviation for Gain

pm2_dev_g

Expected  squared access of  (-(Loss ) + (Average Loss )) over some fixed threshold.

Partial Moment Two Deviation Normal Independent

pm2_ni_dev

Expected  squared access of  ((Loss ) - (Average Loss )) over some fixed threshold for the Loss with independent normally distributed random coefficients.

Partial Moment Two Deviation for Gain Normal Independent

pm2_ni_dev_g

Expected  squared access of  (-(Loss ) + (Average Loss )) over some fixed threshold for the Loss with independent normally distributed random coefficients.

Partial Moment Two Deviation  Normal Dependent

pm2_nd_dev

Expected  squared access of  ((Loss ) - (Average Loss )) over some fixed threshold for the Loss with mutually dependent normally distributed random coefficients.

Partial Moment Two Deviation for Gain Normal Dependent

pm2_nd_dev_g

Expected  squared access of  (-(Loss ) + (Average Loss )) over some fixed threshold for the Loss with mutually dependent normally distributed random coefficients.

Partial Moment Two Max

pm2_max_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). Partial Moment Two Max is calculated by taking Partial Moment Two of the Maximum Loss scenarios.

Partial Moment Two Max  for Gain

pm2_max_pen_g

There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Gain scenarios function is calculated by maximizing losses over Linear -(Loss) functions (over M functions for every scenario). Partial Moment Two Max for Gain is calculated by taking Partial Moment Two of the Maximum Gain scenarios.

Partial Moment Two Max Deviation

pm2_max_dev

There are M Linear Loss scenario functions (every Linear Loss scenario function is defined by a Matrix of Scenarios). A new Maximum Deviation scenarios function is calculated by maximizing losses over (Linear Loss)-(Expected Linear Loss)  functions (over M functions for every scenario). Partial Moment Two Max Deviation is calculated by taking Partial Moment Two of the Maximum Deviation scenarios.

Partial Moment Two Max Deviation for Gain

pm2_max_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 scenarios function is calculated by maximizing losses over -(Linear Loss)+(Expected Linear Loss)  functions (over M functions for every scenario). Partial Moment Two Max Deviation for Gain is calculated by taking Partial Moment Two of the Maximum Deviation for Gain scenarios.

Partial Moment Recourse

pm_pen(recourse(.))

Expected  access of Recourse scenarios over some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

Partial Moment for Gain Recourse

pm_pen_g(recourse(.))

Expected  access of -(Recourse) scenarios over some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

Partial Moment  Deviation Recourse

pm_dev(recourse(.))

Expected  access of (Recourse)-(Expected Recourse) scenarios over some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

Partial Moment Gain Deviation Recourse

pm_dev_g(recourse(.))

Expected  access of -(Recourse)+(Expected Recourse) scenarios over some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

Partial Moment Two Recourse

pm2_pen(recourse(.))

Expected  squared access of Recourse scenarios over some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

Partial Moment Two for Gain Recourse

pm2_pen_g(recourse(.))

Expected squared access of -(Recourse) scenarios over some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

Partial Moment Two Deviation Recourse

pm2_dev(recourse(.))

Expected squared access of (Recourse)-(Expected Recourse) scenarios over some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem for every scenario.

Partial Moment Two Deviation for Gain Recourse

pm2_dev_g(recourse(.))

Expected  squared access of -(Recourse)+(Expected Recourse) scenarios over some fixed threshold. Recourse scenarios are obtained by solving LP at the second stage of two-stage stochastic programming problem.