This calculator helps you compute the probabilities of a logistic distribution given the location and scale parameters. You can find the probability of a value being less than, greater than, or between certain values. The distribution chart shows the probability density function (PDF) and cumulative density function (CDF) of the logistic distribution.
Important:The scale parameter must be positive.
Definition: The logistic distribution is a continuous probability distribution that resembles the normal distribution but has heavier tails. It is symmetric around its location parameter and often used to model growth and decay processes.
Where:
library(tidyverse)
mu <- 2 # location
s <- 0.5 # scale
# p(X < 1)
p_less_than <- plogis(1, location = mu, scale = s)
print(p_less_than) # 0.1192029
# p(X > 2.5)
p_greater_than <- 1 - plogis(2.5, location = mu, scale = s)
print(p_greater_than) # 0.2689414
# P(1 < X < 3)
p_between <- plogis(3, location = mu, scale = s) - plogis(1, location = mu, scale = s)
print(p_between) # 0.7615942
# plot the logistic distribution
x <- seq(mu - 4*s, mu + 4*s, length.out = 1000)
pdf <- dlogis(x, location = mu, scale = s)
df <- tibble(x = x, pdf = pdf)
# Plot PDF
ggplot(df, aes(x = x, y = pdf)) +
geom_line(color = "blue") +
geom_area(data = subset(df, x >= 1 & x <= 3), aes(x = x, y = pdf), fill = "blue", alpha = 0.2) +
labs(title = "Logistic Distribution - PDF",
subtitle = paste0("μ = ", mu, ", s = ", s),
x = "x",
y = "Probability Density") +
annotate("text", x = 3.5, y = 0.3, label = paste0("P(1 < X < 3) = ", round(p_between, 4)), hjust = 0) +
theme_minimal()import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
mu = 2 # location
s = 0.5 # scale
# P(X < 1)
p_less_than = stats.logistic.cdf(1, loc=mu, scale=s)
print(f"P(X < 1) = {p_less_than:.7f}") # 0.1192029
# P(X > 2.5)
p_greater_than = 1 - stats.logistic.cdf(2.5, loc=mu, scale=s)
print(f"P(X > 2.5) = {p_greater_than:.7f}") # 0.2689414
# P(1 < X < 3)
p_between = stats.logistic.cdf(3, loc=mu, scale=s) - stats.logistic.cdf(1, loc=mu, scale=s)
print(f"P(1 < X < 3) = {p_between:.7f}") # 0.7615942
# Plot the logistic distribution
x = np.linspace(mu - 4*s, mu + 4*s, 1000)
pdf = stats.logistic.pdf(x, loc=mu, scale=s)
plt.figure(figsize=(10, 6))
plt.plot(x, pdf, color='blue')
# Shade the area between 1 and 3
mask = (x >= 1) & (x <= 3)
plt.fill_between(x[mask], pdf[mask], alpha=0.2, color='blue')
# Add annotations
plt.annotate(f"P(1 < X < 3) = {p_between:.4f}",
xy=(3.5, 0.3),
xytext=(3.5, 0.3),
ha='left')
plt.title("Logistic Distribution - PDF")
plt.suptitle(f"μ = {mu}, s = {s}")
plt.xlabel("x")
plt.ylabel("Probability Density")
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()This calculator helps you compute the probabilities of a logistic distribution given the location and scale parameters. You can find the probability of a value being less than, greater than, or between certain values. The distribution chart shows the probability density function (PDF) and cumulative density function (CDF) of the logistic distribution.
Important:The scale parameter must be positive.
Definition: The logistic distribution is a continuous probability distribution that resembles the normal distribution but has heavier tails. It is symmetric around its location parameter and often used to model growth and decay processes.
Where:
library(tidyverse)
mu <- 2 # location
s <- 0.5 # scale
# p(X < 1)
p_less_than <- plogis(1, location = mu, scale = s)
print(p_less_than) # 0.1192029
# p(X > 2.5)
p_greater_than <- 1 - plogis(2.5, location = mu, scale = s)
print(p_greater_than) # 0.2689414
# P(1 < X < 3)
p_between <- plogis(3, location = mu, scale = s) - plogis(1, location = mu, scale = s)
print(p_between) # 0.7615942
# plot the logistic distribution
x <- seq(mu - 4*s, mu + 4*s, length.out = 1000)
pdf <- dlogis(x, location = mu, scale = s)
df <- tibble(x = x, pdf = pdf)
# Plot PDF
ggplot(df, aes(x = x, y = pdf)) +
geom_line(color = "blue") +
geom_area(data = subset(df, x >= 1 & x <= 3), aes(x = x, y = pdf), fill = "blue", alpha = 0.2) +
labs(title = "Logistic Distribution - PDF",
subtitle = paste0("μ = ", mu, ", s = ", s),
x = "x",
y = "Probability Density") +
annotate("text", x = 3.5, y = 0.3, label = paste0("P(1 < X < 3) = ", round(p_between, 4)), hjust = 0) +
theme_minimal()import numpy as np
import scipy.stats as stats
import matplotlib.pyplot as plt
mu = 2 # location
s = 0.5 # scale
# P(X < 1)
p_less_than = stats.logistic.cdf(1, loc=mu, scale=s)
print(f"P(X < 1) = {p_less_than:.7f}") # 0.1192029
# P(X > 2.5)
p_greater_than = 1 - stats.logistic.cdf(2.5, loc=mu, scale=s)
print(f"P(X > 2.5) = {p_greater_than:.7f}") # 0.2689414
# P(1 < X < 3)
p_between = stats.logistic.cdf(3, loc=mu, scale=s) - stats.logistic.cdf(1, loc=mu, scale=s)
print(f"P(1 < X < 3) = {p_between:.7f}") # 0.7615942
# Plot the logistic distribution
x = np.linspace(mu - 4*s, mu + 4*s, 1000)
pdf = stats.logistic.pdf(x, loc=mu, scale=s)
plt.figure(figsize=(10, 6))
plt.plot(x, pdf, color='blue')
# Shade the area between 1 and 3
mask = (x >= 1) & (x <= 3)
plt.fill_between(x[mask], pdf[mask], alpha=0.2, color='blue')
# Add annotations
plt.annotate(f"P(1 < X < 3) = {p_between:.4f}",
xy=(3.5, 0.3),
xytext=(3.5, 0.3),
ha='left')
plt.title("Logistic Distribution - PDF")
plt.suptitle(f"μ = {mu}, s = {s}")
plt.xlabel("x")
plt.ylabel("Probability Density")
plt.grid(True, alpha=0.3)
plt.tight_layout()
plt.show()