Skip to main content

Normal distribution

The Normal Distribution, also known as the Gaussian Distribution, is one of the most important and widely used probability distributions in statistics and machine learning. Here are some key characteristics and information about the Normal Distribution:

  1. Shape: The Normal Distribution is symmetric and bell-shaped. It has a single peak at its mean value.


  2. Mean and Median: The mean (average) and median (middle value) of a Normal Distribution are equal. This is typically denoted as μ (mu).


  3. Standard Deviation: The spread or dispersion of data in a Normal Distribution is determined by the standard deviation (σ). A larger standard deviation indicates greater spread.


  4. Probability Density Function (PDF): The probability density function of a Normal Distribution is given by the famous bell-shaped curve formula:

    Normal Distribution PDF

    • The peak of the curve is at the mean (μ).
    • The spread of the curve is determined by the standard deviation (σ).

  5. 68-95-99.7 Rule: In a Normal Distribution:

    • Approximately 68% of the data falls within one standard deviation of the mean (μ ± σ).
    • Approximately 95% falls within two standard deviations (μ ± 2σ).
    • About 99.7% falls within three standard deviations (μ ± 3σ).


  6. Z-Score: The Z-score measures how far away a data point is from the mean in terms of standard deviations. The formula is: Z=X−μσ, where X is the data point.


  7. Use Cases:

    • Many natural phenomena, such as heights, weights, and test scores, follow a Normal Distribution.
    • It is commonly used in hypothesis testing, confidence intervals, and statistical modeling.
    • In machine learning, it's used in algorithms like Gaussian Naive Bayes and for data preprocessing in methods like feature scaling.


  8. Symmetry: The Normal Distribution is symmetric around its mean, meaning that the probabilities of values above the mean are mirrored by the probabilities of values below the mean.


  9. Central Limit Theorem: This theorem states that the sampling distribution of the sample mean becomes approximately normally distributed as the sample size increases, even if the population distribution is not normal. This is fundamental in statistical inference.

In summary, the Normal Distribution is a fundamental concept in statistics and machine learning due to its prevalence in natural phenomena and its mathematical properties, making it a powerful tool for data analysis and modeling.

Labels:

Comments

Post a Comment

Popular posts from this blog

Error: could not find function "read.xlsx" while reading .xlsx file in R

Got this during the execution of following command in R > dat Error: could not find function "read.xlsx" Tried following command > install.packages("xlsx", dependencies = TRUE) Installing package into ‘C:/Users/amajumde/Documents/R/win-library/3.2’ (as ‘lib’ is unspecified) also installing the dependencies ‘rJava’, ‘xlsxjars’ trying URL 'https://cran.rstudio.com/bin/windows/contrib/3.2/rJava_0.9-8.zip' Content type 'application/zip' length 766972 bytes (748 KB) downloaded 748 KB trying URL 'https://cran.rstudio.com/bin/windows/contrib/3.2/xlsxjars_0.6.1.zip' Content type 'application/zip' length 9485170 bytes (9.0 MB) downloaded 9.0 MB trying URL 'https://cran.rstudio.com/bin/windows/contrib/3.2/xlsx_0.5.7.zip' Content type 'application/zip' length 400968 bytes (391 KB) downloaded 391 KB package ‘rJava’ successfully unpacked and MD5 sums checked package ‘xlsxjars’ successfully unpacked ...
Post a Comment
Read more

What is the benefit of using Quantization in LLM

Quantization is a technique used in LLMs (Large Language Models) to reduce the memory requirements for storing and training the model parameters. It involves reducing the precision of the model weights from 32-bit floating-point numbers (FP32) to lower precision formats, such as 16-bit floating-point numbers (FP16) or 8-bit integers (INT8). Bottomline: You can use Quantization to reduce the memory footprint off the model during the training. The usage of quantization in LLMs offers several benefits: Memory Reduction: By reducing the precision of the model weights, quantization significantly reduces the memory footprint required to store the parameters. This is particularly important for LLMs, which can have billions or even trillions of parameters. Quantization allows these models to fit within the memory constraints of GPUs or other hardware accelerators. Training Efficiency: Quantization can also improve the training efficiency of LLMs. Lower precision formats require fewer computati...
Post a Comment
Read more

What is Tensor Parallelism and relationship between Buffer and GPU

  Tensor Parallelism in GPU Tensor parallelism is a technique used to distribute the computation of large tensor operations across multiple GPUs or multiple cores within a GPU .   It is an essential method for improving the performance and scalability of deep learning models, particularly when dealing with very large models that cannot fit into the memory of a single GPU. Key Concepts Tensor Operations : Tensors are multidimensional arrays used extensively in deep learning. Common tensor operations include matrix multiplication, convolution, and element-wise operations. Parallelism : Parallelism involves dividing a task into smaller sub-tasks that can be executed simultaneously. This approach leverages the parallel processing capabilities of GPUs to speed up computations. How Tensor Parallelism Works Splitting Tensors : The core idea of tensor parallelism is to split large tensors into smaller chunks that can be processed in parallel. Each chunk is assigned to a different GP...
Post a Comment
Read more