In merc534/STAT3701-HW3: MercurioRyanTools Package for STAT 3701

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)

This package is my submission for Homework 3 in STAT 3701.

Included in this package are all the functions I have written for class quizzes and homeworks so far. I have omitted redundant functions (e.g. non-GIEMO functions that had GIEMO equivalents).

The first three functions (plottr, filtr, and mylogl) were included in the package submitted for Quiz 2. I have left them in with minimal revision.

Below I briefly demonstrate each function and each attached dataset.

\ \ \ \ \ \/

Package Functions

plottr(dataset,...)

plottr plots the first two columns of a dataframe, with the first column as x and the second as y. The ... argument is passed to geom.point(...) so that color,size, etc. of the data may be changed (I would advise against choosing yellow).

library("MercurioRyanTools")
library(dplyr)
plottr(data1)

x <- data2
y <- 1:30
plotdata <- data.frame(y, x)
plottr(plotdata)
plottr(plotdata, col="yellow", size = 10)

filtr(dataset, col, ...)

filtr will return a specific column from a given dataset. This is really just a wrapper for dplyr::select(). Can call by column number or by column name.

  a <- c(4,5,-14)
  b <- rnorm(3)

  c <- data.frame(a,b)

  filtr(c,col = 1)

  all.equal(filtr(c, col = 'b'), filtr(c, col = 2))

mylogl(x, func, interval)

This function takes a numerical vector $x$, an approximate distribution $func$ and estimates the maximum log-likelihood estimator on a specified range $interval$.

$func$ is a user-defined function of form $function(theta,x)$ where $theta$ is a parameter and $x$ is the numerical vector.

Example functions for argument "fun":

f1 <- function(theta,x)
    {dgamma(x, shape = theta, log = TRUE)}

f2 <- function(theta,x)
    {dcauchy(x, location = theta, log = TRUE)}

f3 <- function(theta,x)
    {dbinom(x, 20, prob = 1 / (1 + exp(- theta)), log = TRUE)}

Calling mylogl()

#Gamma
mylogl (x = rgamma(20,shape = 1), f1, interval = c(0.1,10))
#Cauchy
mylogl (x = rcauchy(20, loc = 5), f2, interval = c(-10,10))
#Binomial
mylogl (x = rbinom(n = 20,size = 20, prob = .80), f3, interval = c(-10,10))

myapply(X, MARGIN, FUN,...)

This function works like $apply()$, but is more limited, since the 'MARGIN' argument must be equal to 1 or 2.

myapply applies a user-supplied function 'FUN' to either all rows ('MARGIN = 1') or all columns ('MARGIN = 2') of some object 'X'

app1 <- data.frame(1:30,2:31)
myapply(app1, 1, sum)
myapply(app1, 2, sum)



myapply(app1, 2, function (x)mylogl(x=x,func = f1, interval = c(0.1,30)))

meanvarsd(d)

Finds the mean, variance, and standard deviation of a discrete probability distribution 'd'.
d\$x should list values with corresponding weights listed in d\$p.

The weights in d\$p must sum to 1.

Returns mean, variance, and standard deviation in that order as a vector of length 3. Works only on data frames

x <- 1:4
p <- c(.1,.2,.3,.4)
dist1 <- data.frame(x,p)

meanvarsd(dist1)

%matlc%

A novelty matrix calculator for the expression $X^T A^{-1} X$

Where the transpose of $X$ is multiplicable by the inverse of $A$.

Here we have a candidate for $A$:

data4[[1]]

And a candidate vector for $X$:

data4[[2]]

The function is used like so:

data4[[1]] %matcalc% data4[[2]]

mstandardize(M)

This simple function standardizes the columns of a matrix in relation to the column's mean and standard deviation.

This should work for any matrix so long as no column has a standard deviation of 0.

data3

This matrix should provide a sufficient example.

round(mstandardize(data3), digits = 2)

\ \ \ \ \ \ \ \/

Package Data

Attached data comes from Charlie's 3701 web files.

data1

Discrete probability distribution. Two columns: x and p.

knitr::kable(head(data1))

data2

Data vector of length 30. Follows cauchy distribution.

knitr::kable(head(data2))

data3

6x4 matrix.

knitr::kable(head(data3))

data4

List with two items. data4[[1]] is a 3x3 matrix. data4[[2]] (apparently called 'x') is a numerical vector of length 3.

knitr::kable(head(data4))

merc534/STAT3701-HW3 documentation built on May 25, 2019, 10:30 p.m.