Binomial Distribution

Functionalities

  • Get a plot of Binomial Distribution B(n,p); n is the total sample size, p is the probability of success / event from the total sample; np=mean, np(1-p)=variance
  • Get the probability of a certain position (at the red point)

Case Example

Suppose we wanted to know the probability of 2 lymphocytes of 10 white blood cells if the probability of any cell being a lymphocyte is 0.2

Please follow the Steps, and Outputs will give real-time analytical results.


Step 1. Select the data source

Mathematical-based, simulated-data-based, or user data-based


Step 2. Set parameters

1. Set Parameters
  • Mean = np
  • Variance = np(1-p)
  • From the example, we know n=10 (10 white blood cells), p=0.2 (the probability of any cell being a lymphocyte)


    2. Change Observed Data

    The observed number is 2 lymphocytes

    When the number of bins is 0, plot will use the default number of bins


    Data point can be separated by , ; /Enter /Tab /Space

    Data be copied from CSV (one column) and pasted in the box

    Missing value is input as NA


    Upload data will cover the example data

    2. Show 1st row as column names?

    3. Use 1st column as row names? (No duplicates)

    Correct separator and quote ensure the successful data input

    Find some example data here

    When the number of bins is 0, plot will use the default number of bins

    Outputs

    Mathematical-based Plot

    Binomial probability plot

    The blue curve is the normal distribution with mean n*p and sd n*p*(1-p). It indicates the normal approximation of binomial distribution.

    Probability at the observed number of success /event (Red-Dot)


    Explanation: the probability of 2 lymphocytes was about 0.03

    Simulation-based Plot

    Histogram from random numbers

    Download Random Numbers

    Sample descriptive statistics

    Distribution of Your Data

    Histogram from upload data

    CDF from upload data

    Sample descriptive statistics


    Poisson Distribution

    Functionalities

    • Draw a plot of Poisson Distribution P(Rate); Rate indicates the expected number of occurrences; Rate = mean =variance
    • Get the probability of a certain position (at the red point)

    Case Example

    Suppose the number of death from typhoid fever over a 12 month period is Poisson distributed with parameter rate=2.3. What is the probability distribution of the number of deaths over a 6-month period?

    Please follow the Steps, and Outputs will give real-time analytical results.


    Step 1. Select the data source

    Mathematical-based, simulated-data-based, or user data-based


    Step 2. Set parameters

    1. Set Parameters

    From the example, the rate is 2.3 and the duration of the rate is 12 months


    2. Change Observed Data

    The observed is <= 5, and we wanted to know the cumulated probability after 5 months, which means 1 - cumulated probability of 0-5 months

    When the number of bins is 0, plot will use the default number of bins


    Data point can be separated by , ; /Enter /Tab /Space

    Data be copied from CSV (one column) and pasted in the box

    Missing value is input as NA


    Upload data will cover the example data

    2. Show 1st row as column names?

    3. Use 1st column as row names? (No duplicates)

    Correct separator and quote ensure the successful data input

    Find some example data here

    When the number of bins is 0, plot will use the default number of bins

    Outputs

    Mathematical-based Plot

    The blue curve is the normal distribution with mean=rate and sd=rate. It indicates the normal approximation of binomial distribution.

    Poisson probability plot

    Probability at the observed number of occurrences (Red-Dot)


    Explanation: the probability distribution until 5 month was 0.97. Thus, the probability distribution after 6 months was about 0.03

    Histogram from random numbers

    Download Random Numbers

    Sample descriptive statistics

    Distribution of Your Data

    Histogram from upload data

    Sample descriptive statistics

    CDF from upload data