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Hi everyone, I'm glad you're here. In this blog post, I'm going to talk about one of the most useful and powerful classes in scipy.stats: rv_continuous. This class allows you to define and work with continuous random variables in Python. You can use it to model various phenomena in science, engineering, economics, and more.
But what is a continuous random variable? And what is rv_continuous? How can you use it to create and manipulate distributions? These are some of the questions that I will answer in this blog post. I hope you will find it informative and interesting. Let's get started!
A continuous random variable is a variable that can take any value in a certain range, such as the height of a person, the weight of a fruit, or the time it takes to finish a task. Unlike discrete random variables, which can only take specific values, such as the number of heads in a coin toss, continuous random variables can take infinitely many values.
To work with continuous random variables in Python, we can use the rv_continuous class from scipy.stats. This class provides methods for computing the probability density function (pdf), the cumulative distribution function (cdf), the inverse cdf (ppf), and generating random samples (rvs) of any distribution that inherits from it. You can also calculate moments, entropy, and other statistics of the distribution using rv_continuous methods.
The pdf of a continuous random variable tells us how likely it is to take a certain value. For example, the pdf of a normal distribution looks like a bell-shaped curve, and it tells us that values near the mean are more likely than values far away from the mean. The cdf of a continuous random variable tells us how likely it is to take a value less than or equal to a certain value. For example, the cdf of a normal distribution starts from zero and increases to one as we move from left to right along the x-axis. The ppf of a continuous random variable is the inverse of the cdf. It tells us what value corresponds to a given probability. For example, the ppf of a normal distribution tells us what value is one standard deviation away from the mean if we give it a probability of 0.84. The rvs of a continuous random variable generates random samples from the distribution. For example, the rvs of a normal distribution gives us random numbers that follow the normal distribution.
Some examples of distributions that are subclasses of rv_continuous are normal, uniform, exponential, gamma, beta, and many more. You can find a list of all the available continuous distributions in scipy.stats here. You can also create your own custom distribution by subclassing rv_continuous and overriding the _pdf or _cdf method. You can find more details and examples on how to do that here.
To fit a continuous distribution to some data, you can use the fit method of rv_continuous. This method returns the optimal values of the shape parameters, the location parameter, and the scale parameter that best fit the data. For example, if you have some data that follows a beta distribution, you can use beta.fit(x) to get the estimates of the parameters a, b, loc, and scale.
Example(Simulates the weight of a fruit)
To create a code that simulates the weight of a fruit, we need to choose a distribution that fits the data well. One possible distribution that can model the weight of a fruit is the normal distribution, which is also called the Gaussian distribution or the bell curve. The normal distribution is defined by two parameters: the mean and the standard deviation. The mean is the average value of the distribution, and the standard deviation is a measure of how spread out the values are around the mean
To use the normal distribution in Python, we can import the scipy.stats module, which provides various statistical functions and distributions. We can then use the norm class to create a normal distribution object with a given mean and standard deviation. For example, if we want to create a normal distribution with mean 150 grams and standard deviation 20 grams, we can write:
import scipy.stats as stats
fruit_weight = stats.norm(150, 20)We can then use the methods of the norm class to calculate various properties of the distribution, such as the probability density function (pdf), the cumulative distribution function (cdf), and the inverse cdf (ppf). We can also generate random samples from the distribution using the rvs method. For example, if we want to generate 10 random samples of fruit weight from the normal distribution, we can write:
samples = fruit_weight.rvs(size=10)
print(samples)This will print an array of 10 numbers that represent the weight of 10 fruits in grams. These numbers will vary each time we run the code, because they are randomly generated.
We can also plot the pdf of the normal distribution using matplotlib.pyplot, which is a module that allows us to create and customize plots in Python. We can import matplotlib.pyplot as plt and then use plt.plot to plot an array of x values versus an array of y values. We can use np.linspace to create an array of x values that span a certain range, and then use fruit_weight.pdf to calculate the corresponding y values. We can also add a title and labels to the plot using plt.title, plt.xlabel, and plt.ylabel. Finally, we can use plt.show to display the plot. For example, if we want to plot the pdf of the normal distribution from 100 grams to 200 grams, we can write:
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(100, 200, 100) # Create an array of 100 values from 100 to 200
y = fruit_weight.pdf(x) # Calculate the pdf of the normal distribution at each value of x
plt.plot(x, y) # Plot x versus y
plt.title("PDF of the normal distribution for fruit weight") # Add a title to the plot
plt.xlabel("Weight (grams)") # Add a label to the x-axis
plt.ylabel("Probability density") # Add a label to the y-axis
plt.show() # Show the plot>This will produce a plot like this:
You can find the result in Github gist, here.
I’m happy to hear that you enjoyed our journey of learning about rv_continuous, a class in scipy.stats that allows you to define and work with continuous random variables. We have covered a lot of topics, such as what is a continuous random variable, how to create and manipulate distributions using rv_continuous, how to plot and fit distributions using matplotlib.pyplot, and how to generate code examples and explanations using my own words and knowledge.
I hope you found this blog post informative and interesting. If you did, please share it with your friends and colleagues who might be interested in scipy.stats or Python programming. And if you have any feedback or questions, please leave a comment below or contact me through my email. I would love to hear from you.
Thank you for reading my blog post on rv_continuous. I hope to see you again soon
