# bigfp: Compute the numerical integration by the trapezoidal rule. In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

 bigfp R Documentation

## Compute the numerical integration by the trapezoidal rule.

### Description

See page 220 of Vinod (2008) “Hands-on Intermediate Econometrics Using R,” for the trapezoidal integration formula needed for stochastic dominance. The book explains pre-multiplication by two large sparse matrices denoted by `I_F, I_f`. Here we accomplish the same computation without actually creating the large sparse matrices. For example, the `I_f` is replaced by `cumsum` in this code (unlike the R code in my textbook).

### Usage

``````bigfp(d, p)
``````

### Arguments

 `d` A vector of consecutive interval lengths, upon combining both data vectors `p` Vector of probabilities of the type 1/2T, 2/2T, 3/2T, etc. to 1.

### Value

Returns a result after pre-multiplication by `I_F, I_f` matrices, without actually creating the large sparse matrices. This is an internal function.

### Note

This is an internal function, called by the function `stochdom2`, for comparison of two portfolios in terms of stochastic dominance (SD) of orders 1 to 4. Typical usage is: ```sd1b=bigfp(d=dj, p=rhs) sd2b=bigfp(d=dj, p=sd1b) sd3b=bigfp(d=dj, p=sd2b) sd4b=bigfp(d=dj, p=sd3b)```. This produces numerical evaluation vectors for the four orders, SD1 to SD4.

### Author(s)

Prof. H. D. Vinod, Economics Dept., Fordham University, NY

### References

Vinod, H. D.', 'Hands-On Intermediate Econometrics Using R' (2008) World Scientific Publishers: Hackensack, NJ. https://www.worldscientific.com/worldscibooks/10.1142/6895

generalCorr documentation built on May 1, 2023, 9:06 a.m.