# T.INV Function

Calculates the left-tailed student's t-distribution

Calculates the left-tailed student's t-distribution

The TINV Excel Function is categorized under Statistical functions. It will calculate the left-tailed student’s t-distribution. The student’s t-distribution is a continuous probability distribution that is frequently used in testing hypotheses on small sample data sets.

As a financial analyst, the T.INV function is used in portfolio risk analysis, particularly, the risk-return relationship of a portfolio. The function is often used when the sample size is smaller, i.e., when a portfolio comprises 20 stocks or 5 asset classes only.

=**T.INV(probability,deg_freedom)**

The T.INV function uses the following arguments:

**Probability**(required argument) – It is the probability associated with the Student’s T Distribution.**Deg_freedom**(required argument) – It is the number of degrees of freedom with which to characterize the distribution.

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To understand the uses of the T.INV function, let us consider a few examples:

Suppose we are given the following data:

If we want to calculate the value of the function for a probability of 0.20, the formula to use is:

We get the result below:

So, the left-tailed inverse of the student’s t-distribution with a probability of 20% and 5 degrees of freedom is -0.920.

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Suppose we are given the following data:

If we want to calculate the value of the function for a probability of 0.80, the formula to use is:

We get the result below:

So, the left-tailed inverse of the student’s t-distribution with a probability of 80% and 10 degrees of freedom is 0.879.

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- #NUM! error – Occurs when:
- The given probability is less than or to zero or is greater than one.
- The given deg_freedom is less than 1.

- #VALUE! error – Occurs when one or both of the supplied arguments are non-numeric.
- If deg_freedom is not an integer, it is truncated.

**Click here to download the sample Excel file**

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