Fréchet distribution calculator
Enter a point and the three numbers of a Fréchet distribution: at the point 1, with shape 2, scale 1 and location 0, the cumulative probability is 0.367879 and the density 0.735759. The mean appears once the shape exceeds 1. Free in your browser.
- Free
- Runs in your browser
- No sign-up
- Your data stays on your device
Run — free
Worked example
- X
- 1
- Alpha
- 2
- S
- 1
- M
- 0
- Decimal places
- 6
- PDF file
- 0.735759
- Cdf
- 0.367879
- Mean
- 1.772454
PDF/CDF of Fréchet (Type II extreme value); mean when α>1. Search intent: frechet distribution calculator. No network calls or random seeds are required. Failed jobs are not billed.
What the three Fréchet numbers do
The Fréchet distribution is the Type II member of the extreme value family. Three numbers define it. The shape α, which must be greater than zero, sets the profile of the curve. The scale s, also positive, stretches it. The location m slides the whole curve along the axis. You choose a point x above zero and the calculator gives you two values for it: the probability density at that point and the cumulative probability, which is the chance of observing a value no larger than x. When α is greater than 1 it also gives the mean of the distribution. With x of 1, α of 2, scale 1 and location 0, the density is 0.735759, the cumulative probability 0.367879 and the mean 1.772454.
Reading the result without the usual slips
The cumulative probability follows a single rule: take x minus the location, divide by the scale, raise that to the power minus α, and the result is the exponential of its negative. The density is not a probability on its own, so compare it only with other densities. Do not expect a mean when α is 1 or less, because it does not exist there. Every value is checked before any arithmetic, so a scale or shape of zero is refused instead of producing a misleading number. If you ask for a fixed number of decimals, the exact result is rounded once, with halves going up, and the same inputs always give the same answer.
When to use it
Use when search intent matches. PDF/CDF of Fréchet (Type II extreme value); mean when α>1. English-only delivery; Nitro hydrates other locales.
No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required.
Failed jobs are not billed.
What you can do with it
Teaching
Pinned goldens.
FAQ
What is the Fréchet distribution?
It is the Type II extreme value distribution, defined by a shape α, a scale s and a location m. You give a point x and get its probability density, its cumulative probability and, when α is above 1, its mean.
How is the Fréchet cumulative probability calculated?
Subtract the location from x, divide by the scale, raise the result to the power minus α, change its sign and take the exponential. With x of 1, α of 2, scale 1 and location 0 that gives 0.367879.
Why is there no mean for some shape values?
The Fréchet mean only exists when the shape α is greater than 1; below that it is not finite. So the calculator reports a mean only in that case: with α of 2, scale 1 and location 0 it is 1.772454.
What is the difference between the density and the cumulative probability?
The density tells you how concentrated the distribution is at the point x: 0.735759 in the example with α of 2 and scale 1. The cumulative probability is the chance of a value at or below x: 0.367879 in the same example.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/stat/frechet-dist \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"x":1.5,"alpha":2}'const res = await fetch("https://api.kit.forhosting.com/stat/frechet-dist", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"x": 1.5,
"alpha": 2
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/stat/frechet-dist",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"x": 1.5,
"alpha": 2
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/stat/frechet-dist", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"x":1.5,"alpha":2}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"x":1.5,"alpha":2}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/stat/frechet-dist", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"x": 1.5,
"alpha": 2
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "stat.frechet_dist",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested.
How it works
PDF/CDF of Fréchet (Type II extreme value); mean when α>1. CDF=exp(-( (x-m)/s )^{-α}). No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input.
Inputs, limits and rounding
Optional decimals use half-up once. Optional output fields are omitted, never null. No network calls or random seeds are required. Failed jobs are not billed. No network calls or random seeds are required. Failed jobs are not billed. Provide required JSON fields with DOM-safe names. Invalid types raise invalid_input. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested.
When to use it
The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested. The calculator is free in the browser, deterministic, and identical on the API path. Inputs are validated before arithmetic so invalid payloads fail with invalid_input. Half-up rounding is applied once from raw IEEE values when decimals are requested.
Integration use cases
Quick check
Free widget.
Automation
API same JSON.
Technical questions
Free?
Yes tier A.
Network?
No.
Bad input?
invalid_input.
API?
Yes.
Locales?
EN-only; Nitro hydrates.