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Logistic Functions in R: A Tutorial

In this tutorial, we will explore the logistic functions in R, including the density, cumulative distribution function, quantile function, and random number generation.

We will use the dlogis, plogis, qlogis, and rlogis functions to demonstrate each of these functions.

Example 1: Logistic Density in R (dlogis Function)

To begin, we need to create a sequence of quantiles:

x_dlogis <- seq(-10, 10, by = 0.1)

Then, we can apply the dlogis function:

y_dlogis <- dlogis(x_dlogis)

To visualize the output, we can plot the values:

plot(y_dlogis)

This will produce a plot of the logistic probability density function (PDF).

Example 2: Logistic Cumulative Distribution Function (plogis Function)

For the cumulative distribution function (CDF), we need to create a sequence of quantiles:

x_plogis <- seq(-10, 10, by = 0.1)

Then, we can apply the plogis function:

y_plogis <- plogis(x_plogis)

To visualize the output, we can plot the values:

plot(y_plogis)

This will produce a plot of the logistic cumulative distribution function (CDF).

Example 3: Logistic Quantile Function (qlogis Function)

For the quantile function, we need to create a sequence of probabilities:

x_qlogis <- seq(0, 1, by = 0.01)

Then, we can apply the qlogis function:

y_qlogis <- qlogis(x_qlogis)

To visualize the output, we can plot the values:

plot(y_qlogis)

This will produce a plot of the logistic quantile function.

Example 4: Generating Random Numbers (rlogis Function)

To generate random numbers with a logistic distribution, we need to set a seed for reproducibility and a sample size:

set.seed(123)
N <- 10000

Then, we can apply the rlogis function:

y_rlogis <- rlogis(N)

We can print the values to the RStudio console:

y_rlogis

And create a histogram of the output:

hist(y_rlogis, breaks = 70, main = "")

This will produce a plot of the logistic density.

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