Running a rgeom Sample and Storing the Mean and SD of Each Replication

In this article, we will explore how to run a sample using the rgeom function in R and store the mean and standard deviation (SD) of each replication. We will also discuss why the previous approach may not have worked correctly.

Introduction

The rgeom function is used to generate random samples from a geometric distribution. The geometric distribution models the number of failures before the first success, where each trial is independent and has a constant probability of success. In this article, we will use the rgeom function to generate random samples with a specified number of trials (n) and probability of success (prob). We will then calculate the mean and SD of each replication.

Setting Up

To start, let’s set up our R environment by loading the necessary libraries. In this case, we only need the base R library, which includes all the essential functions for statistical analysis.

# Load the necessary library
library(base)

Generating Random Samples

Next, we will generate random samples using the rgeom function. The rgeom function takes two arguments: n, the number of trials, and prob, the probability of success. We can use the following code to generate a single sample:

# Generate a random sample with n = 100 and prob = 0.2
samp <- rgeom(100, prob = 0.2)

Calculating the Mean and SD

To calculate the mean and SD of each replication, we can use the mean() and sd() functions in R.

# Calculate the mean and SD of the sample
mean_samp <- mean(samp)
sd_samp <- sd(samp)

However, this approach has a limitation. If we want to generate multiple samples and calculate their means and SDs separately, we will need a more efficient way to store the results.

Using a Vectorized Approach

One approach is to use a vectorized function that takes in n and prob, generates random samples, calculates the mean and SD of each sample, and returns the results as a list.

# Define a function that generates random samples with n trials and prob probability
# of success
set.seed(123)
samp_geom <- function(n, prob) {
  # Generate a random sample with n trials and prob probability of success
  samp <- rgeom(n, prob)
  
  # Calculate the mean and SD of the sample
  mean_samp <- round(mean(samp), 2)
  sd_samp <- round(sd(samp), 2)
  
  # Return the results as a list
  return(list(mean = mean_samp, sd = sd_samp))
}

# Generate multiple random samples with n = 100 and prob = 0.2
n_rep <- 5
samps <- replicate(n_rep, samp_geom(100, .2))

# Extract the means and SDs from the list
geom_means <- unlist(samps["mean", ])
geom_sd <- unlist(samps["sd", ])

This approach is more efficient than using a for loop to calculate the mean and SD of each sample separately. It also allows us to store the results in separate vectors.

Using a For Loop (But Don’t)

Although the previous approach is more efficient, we can still explore how to use a for loop to calculate the mean and SD of each sample. Here’s an example:

# Initialize empty vectors to store the means and SDs
geom_means <- rep(NA, 500)
geom_sd <- rep(NA, 500)

# Use a for loop to generate random samples with n = 100 and prob = 0.2
# Calculate the mean and SD of each sample
for (i in 1:500) {
  samp <- rgeom(100, prob = 0.2)
  geom_means[i] <- round(mean(samp), 2)
  geom_sd[i] <- round(sd(samp), 2)
}

However, this approach has a limitation. The results may not be accurate due to the random nature of the samples. Additionally, it can be slow for large numbers of trials.

Conclusion

In conclusion, we have explored how to run a sample using the rgeom function in R and store the mean and standard deviation (SD) of each replication. We discussed two approaches: using a vectorized function and using a for loop. The vectorized approach is more efficient and allows us to store the results in separate vectors. However, the for loop approach can still be useful in certain situations.

Last modified on 2024-01-01