In qf1999/StatComp21039: Provide several functions for the final homework of the 'Statistical Computing' course in 2021 fall

knitr::opts_chunk$set(echo = TRUE)

Stochastic dominance tests for risk averters

Definition of risk averters: ${u:(-1)^i·u^{(i)}\le0,i=1,2,3}$ where $u^{(i)}$ is the ith derivative of u. u is utility functions.

For two random variables Y and Z with Observed data ‘data1’ and ‘data2’, we can use this function ‘sdfra’ which means stochastic dominance for risk averters to test if Y dominance or dominanced by Z in first, second or third order. Both data1 and data2 should be a column of numbers. And B is the times for bootstrap, it has a default value of 2000.

result <- sdfra(data1, data2, B)

Output is a list that contains tests result for FSD, SSD, TSD and some statistics, we can call the result with 'sd', 'TA' and 'bound'.

For risk averters, if sd[i]=1 then random variables Y dominance Z in the ith order. If sd[i]=-1 then random variables Y is dominanced by Z in the ith order.If sd[i]=0 then random variables Y and Z don't have dominance relation.

'TA' is a matrix of 3x200, shows the Stochastic dominance statistic on the select point. 'Bound' is a matrix of 5x3 shows the statistic we got to compare the sd relation between Y and Z.

Stochastic dominance tests for risk seekers

Definition of risk seekers: ${u:u^{(i)}\ge0,i=1,2,3}$ where $u^{(i)}$ is the ith derivative of u. u is utility functions.

Similarly, for two random variables Y and Z with Observed data ‘data1’ and ‘data2’, we can use this function ‘sdfrs’ which means stochastic dominance for risk seekers to test if Y dominance or dominanced by Z in first, second or third order. Both data1 and data2 should be a column of numbers. And B is the times for bootstrap, it has a default value of 2000.

result <- sdfrs(data1, data2, B)

Output is a list that contains tests result for FSD, SSD, TSD and some statistics, we can call the result with 'sd', 'TD' and 'bound'.

For risk seekers, if sd[i]=1 then random variables Y dominance Z in the ith order. If sd[i]=-1 then random variables Y is dominanced by Z in the ith order.If sd[i]=0 then random variables Y and Z don't have dominance relation.

'TD' is a matrix of 3x200, shows the Stochastic dominance statistic on the select point. 'Bound' is a matrix of 5x3 shows the statistic we got to compare the sd relation between Y and Z.

qf1999/StatComp21039 documentation built on Dec. 23, 2021, 11:11 p.m.