May 2024

The Zipf distribution, also sometimes referred to as the zeta distribution, is a discrete probability distribution used to model scenarios where the frequency of an item is inversely proportional to its rank. It’s implemented in NumPy using the np.random.zipf function. Here’s a breakdown of the key characteristics and its application in NumPy: Core Idea (Zipf’s…

The Pareto distribution, also known as the Pareto II or Lomax distribution, is a continuous probability distribution used to model situations where few events have large values, and many events have smaller values. or A distribution following Pareto’s law i.e. 80-20 distribution (20% factors cause 80% outcome). It’s implemented in NumPy using the np.random.pareto function.…

The Rayleigh distribution is a probability distribution used to model the magnitudes of random vectors whose components follow independent Gaussian (normal) distributions. It’s relevant in various fields like signal processing, physics, and oceanography. NumPy provides the np.random.rayleigh function to generate random samples from this distribution. Here’s a detailed breakdown of the Rayleigh distribution and its…

The chi-square distribution is a fundamental probability distribution used in hypothesis testing, particularly in chi-square tests. It’s implemented in Python’s NumPy library using the np.random.chisquare function. Properties: Applications: Generating Random Samples with np.random.chisquare: Parameters: Important Note: While np.random.chisquare generates samples from the chi-square distribution, it’s essential to use this within the context of chi-square tests…

The exponential distribution is a probability distribution used to model the time between events that happen randomly and independently at a constant rate. It’s implemented in Python’s NumPy library using the np.random.exponential function. Here’s a breakdown of the key points: Properties: Applications: Generating Random Samples with np.random.exponential: Output Parameters:

The multinomial distribution in Python’s NumPy library is represented by the np.random.multinomial function. It’s used to generate random samples that represent the number of times events from several categories occur in a fixed number of trials. Here’s a detailed explanation: Concept: Generalizes the binomial distribution (two possible outcomes) to scenarios with multiple (>2) possible categories.Models…

The logistic distribution, also known as the sigmoid distribution, is a continuous probability distribution in Python’s NumPy library. Logistic Distribution is used to describe growth. Used extensively in machine learning in logistic regression, neural networks etc. It’s modeled by the numpy.random.logistic function and is useful for representing S-shaped curves where the probability of an event…

The uniform distribution is represented by the numpy.random.uniform function. It’s used to generate random numbers that are uniformly distributed over a specified interval. Used to describe probability where every event has equal chances of occuring. Here’s a breakdown of what it does: Functionality: Generates random floating-point numbers.Numbers are distributed uniformly across a half-open interval [low,…