1. What is the Confidence Interval of Variate?

The Confidence Interval of Variate calculates the bounded value x1 using Gumbel's method, which defines the range of effective measurement increments about a central point for the distribution.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( x_T \) — Variate 'X' with a Recurrence Interval of a random hydrologic series with a return period
• \( f_c \) — Function of Confidence Probability defined by normal variates
• \( S_e \) — Probable Error, the half-range of an interval about a central point for the distribution

Explanation: This formula calculates the limits about the calculated value between which the true value can be said to lie, using Gumbel's method for defining the range of effective measurement increments.

3. Importance of Confidence Interval Calculation

Details: Calculating confidence intervals is crucial for determining the range within which the true value of a variate is likely to fall, providing a measure of uncertainty in statistical estimates and helping in making reliable predictions.

4. Using the Calculator

Tips: Enter the Variate 'X' with a Recurrence Interval, Function of Confidence Probability, and Probable Error values. All values must be valid numerical inputs.

5. Frequently Asked Questions (FAQ)

Q1: What does the Value of 'x1' Bounded to Variate 'Xt' represent?
A: It represents the limits about the calculated value between which the true value can be said to lie with a certain confidence level.

Q2: How is the Function of Confidence Probability determined?
A: The Function of Confidence Probability is defined by normal variates and depends on the desired confidence level for the interval estimation.

Q3: What is Probable Error in this context?
A: Probable Error is the half-range of an interval about a central point for the distribution and in Gumbel's method it defines the range of effective measurement increments.

Q4: When should this calculation be used?
A: This calculation is particularly useful in hydrological studies and statistical analysis where estimating the range of true values with a certain confidence level is important.

Q5: Are there limitations to this method?
A: The accuracy depends on the proper determination of the input parameters and assumes that the underlying statistical assumptions of Gumbel's method are met.