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Open toolNegative Binomial Calculator
Find the negative-binomial probability that the r-th success occurs on attempt n. Provide Required successes r, Total attempts until r-th success n, Independent success probability p to compute results directly in your browser. Trial-count convention n>=r; formula C(n-1,r-1)*p^r*(1-p)^(n-r). Endpoints p=0 and 1 are handled explicitly, no independence inference. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
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Enter the inputs, then select Calculate.
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How the Negative Binomial Calculator Works & Core Formula
The Negative Binomial Calculator evaluates Required successes r, Total attempts until r-th success n, Independent success probability p in client-side JavaScript using the deterministic rule below and updates the output panel immediately without uploading data to a server.
Find the negative-binomial probability that the r-th success occurs on attempt n.
Trial-count convention n>=r; formula C(n-1,r-1)*p^r*(1-p)^(n-r). Endpoints p=0 and 1 are handled explicitly, no independence inference. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
Negative Binomial Calculator Quick Reference & Input Guide
Review the input parameters, allowed value ranges, and worked reference cases for the Negative Binomial Calculator below before running your calculation.
| Parameter / Scenario | Default / Sample Value | Rule or Allowed Range | Output / Usage Note |
|---|---|---|---|
| Input: Required successes r | 2 | Range: 1 to 10000 | Required workspace parameter |
| Input: Total attempts until r-th success n | 5 | Range: 1 to 10000 | Required workspace parameter |
| Input: Independent success probability p | 0.5 | Range: 0 to 1 | Required workspace parameter |
| Worked Case 1: Baseline run (Required successes r = 2) | Preloaded / test values | Find the negative-binomial probability that the r-th success occurs on attempt n | Required successes r = 2; Total attempts until r-th success n = 5; Independent success probability p = 0.5. The displayed output is P(N=n): 0.125 Probability percent: 12.5%. |
| Worked Case 2: Comparison scenario (negative binomial distribution calculator) | Preloaded / test values | Find the negative-binomial probability that the r-th success occurs on attempt n | Required successes r = 1; Total attempts until r-th success n = 3; Independent success probability p = 0.5. The displayed output is P(N=n): 0.125 Probability percent: 12.5%. |
Step-by-Step Guide to Using the Negative Binomial Calculator
Follow these three steps to configure Required successes r, Total attempts until r-th success n, Independent success probability p, verify unit and boundary rules, and export your Negative Binomial Calculator output.
Enter required successes r
Enter required successes r. Allowed range: 1 to 10000. Whole numbers only.
Input and settings
Complete the other inputs
Set total attempts until r-th success n, independent success probability p. Trial-count convention n>=r; formula C(n-1,r-1)*p^r*(1-p)^(n-r).
Tool result
Calculate and read the output
Select Calculate to see the trial-count probability and percentage. Copy result copies this text; Download saves it as a TXT file.
Review the details
Practical Worked Examples for Negative Binomial Calculator
These concrete scenarios illustrate how the Negative Binomial Calculator processes baseline inputs, comparison checks, and boundary constraints.
Baseline run (Required successes r = 2)
Required successes r = 2; Total attempts until r-th success n = 5; Independent success probability p = 0.5. The displayed output is P(N=n): 0.125 Probability percent: 12.5%.
Comparison scenario (negative binomial distribution calculator)
Required successes r = 1; Total attempts until r-th success n = 3; Independent success probability p = 0.5. The displayed output is P(N=n): 0.125 Probability percent: 12.5%.
Boundary & unit check (Negative Binomial Calculator)
When solving for 'negative binomial calculator', verify that Required successes r, Total attempts until r-th success n, Independent success probability p use consistent units and stay within the documented scope: Trial-count convention n>=r; formula C(n-1,r-1)*p^r*(1-p)^(n-r). Endpoints p=0 and 1 are handled explicitly, no independence inference. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur.
How to Read and Verify the Negative Binomial Calculator Output
The output panel reports the exact result derived from Required successes r, Total attempts until r-th success n, Independent success probability p alongside any unit or formatting notes.
The result is the trial-count probability and percentage. Explore the attempt on which a chosen success count is reached.
The selected convention counts all attempts, including the required successful attempts.
Numerical output shows up to 12 significant digits. Floating-point arithmetic and display rounding can affect the last digits.
- Example input
- Required successes r = 2; Total attempts until r-th success n = 5; Independent success probability p = 0.5
- Example output
- P(N=n): 0.125 Probability percent: 12.5%
Scope Limits, Accuracy Assumptions & Related Everyday Math Tools
Review these boundary constraints and validation rules before relying on the Negative Binomial Calculator output.
Operational scope: Trial-count convention n>=r; formula C(n-1,r-1)*p^r*(1-p)^(n-r). Endpoints p=0 and 1 are handled explicitly, no independence inference. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur. Inputs that violate minimum/maximum bounds or required format rules are rejected with a clear diagnostic prompt.
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Open toolFrequently Asked Questions About Negative Binomial Calculator
Answers about using Negative Binomial Calculator and understanding its results.
What formula or rule does the Negative Binomial Calculator use?
The Negative Binomial Calculator applies the rule: Find the negative-binomial probability that the r-th success occurs on attempt n. Enter Required successes r, Total attempts until r-th success n, Independent success probability p into the workspace and the tool computes the exact output in your browser.
What input parameters and units are required for Negative Binomial Calculator?
Yes. Provide Required successes r, Total attempts until r-th success n, Independent success probability p using the documented units and format shown in the quick reference table above. Preloaded default values let you test the workflow immediately.
What are the accuracy limits and boundary assumptions for Negative Binomial Calculator?
Trial-count convention n>=r; formula C(n-1,r-1)*p^r*(1-p)^(n-r). Endpoints p=0 and 1 are handled explicitly, no independence inference. Inputs and results use floating-point numbers; output shows up to 12 significant digits. Rounding can occur. Confirm that your inputs fall within the allowed ranges before exporting the result.
Is the Negative Binomial Calculator free and does it keep my inputs private?
Yes. All calculations for the Negative Binomial Calculator execute 100% locally in your browser's JavaScript runtime. No inputs or results are uploaded to any external server.
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