R-functions

This program consists of R functions that compute statistical concepts such as confidence intervals, p-values, maximum likelihood estimation, and optimal overbooking thresholds. This was created for my (Applied Statistical Methods) course.

Author:

Cristiana Eagen

Built With:

• R
• R packages: stats, graphics, grDevices

Functions:

• ntickets.R: This function calculates the number of tickets to be sold when the number of seats in the flight is N and the probability of a "show" is p and gamma is the probability a plane will be truly overbooked (more people show than there are seats).
• myhyper.R: Takes random samples and makes a barplot of successes.
• mymaxlikg.R: This function computes the maximum likelihood estimate for a given likelihood function over a range of theta values.
• mycltp.R: This function demonstrates the Central Limit Theorem. It gets random samples from a Poisson distribution, calculates the sample means, and generates histograms of these means. It also compares the sample distribution to a theoretical normal distribution and includes a bar plot of the sampled Poisson values.
• mypvalue.R: This function calculates the p-value, displays the corresponding t-distribution, and gives the graph with the p-value areas.
• myci.R: This function calculates a (1 - alpha) * 100% confidence interval for the mean of a single sample.
• myncurve.R: Displays a normal curve, shades the area from −∞ to a given x-value, and returns the probability P(X ≤ a).

How to run the code:

• Clone this repository
• Load individual .R files into RStudio.
• Call the functions using example values.

Example:

ntickets(N = 400, gamma = 0.02, p = 0.95)