Mean Kurtosis Calculator

Arithmetic directional mean diffusion kurtosis under independently established uniform spherical quadrature, equally weighted directions, not scalar raw sample distribution kurtosis or full tensor fit. Actual independently matched observations/units and protocol, not diagnosis, causal mechanism, clinical decision or validated individual prediction.

Description

A mean diffusion-kurtosis estimate can use an arithmetic average when directional samples represent an independently established uniform spherical quadrature.

A mean diffusion-kurtosis estimate can use an arithmetic average when directional samples represent an independently established uniform spherical quadrature.^[1]

This tool averages those supplied samples without fitting a tensor or computing distribution kurtosis.

When to use Mean Kurtosis Calculator

This tool averages those supplied samples without fitting a tensor or computing distribution kurtosis.

How to use Mean Kurtosis Calculator and how it works

Prepare independent directional kurtosis samples, using the input definitions and matching units below.
Enter the required fields and run Mean Kurtosis Calculator.
Read result.value using the units, signs and ordering explained below.
Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.

Input field	Meaning	Value type	Requirement
actualIndependentDirectionalKurtosisSamples	Actual Independent Directional Kurtosis Samples. Use the units and matching context stated in the calculation below.	array of number	Required; other constraints below

Require a nonempty list of finite independently established directional diffusion-kurtosis samples. Return their arithmetic mean without rejecting signed values or applying angular weights. Equal weights are appropriate only for the externally established uniform spherical quadrature; no kurtosis tensor or raw distribution moment is fitted.

meanDirectionalKurtosis=sum(directionalKurtosis)/N

Apply the input ordering, units and branch conditions stated above.

Output field	Meaning	Value type
result	Object containing the calculated or selected fields below.	object
result.value	Numeric model result on the ratio, score, constant or density basis explained above.	number

json

{
  "input": {
    "actualIndependentDirectionalKurtosisSamples": [
      1,
      2,
      3
    ]
  },
  "output": {
    "result": {
      "value": 2
    }
  }
}

Limitations and assumptions

The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.

All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.

Alternative or Complementary methods

Use Neurite Density Index Calculator for a complementary operation: A neurite-density index depends on the diffusion acquisition, compartment model and parameter interpretation.

Use Radial Kurtosis Calculator for a complementary operation: Radial diffusion kurtosis depends on tensor fitting and the direction convention perpendicular to a qualified axis.

References

Mean Kurtosis Calculator — tool.io

Similar or alternative tools

Neurite Density Index Calculator
A neurite-density index depends on the diffusion acquisition, compartment model and parameter interpretation.
Radial Kurtosis Calculator
Radial diffusion kurtosis depends on tensor fitting and the direction convention perpendicular to a qualified axis.