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Maximum likelihood estimators of the Cauchy distribution cannot be written in closed form since they are given as the roots of higher-degree polynomials. Please see the link for details.

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Which distribution do not have mean?

The Cauchy or Cauchy-Lorentz distribution. The ratio of two Normal random variables has a C-L distribution.


What is a cauchy sequence?

(xn) is Cauchy when abs(xn-xm) tends to 0 as m,n tend to infinity.


What country was Augustin Cauchy born in?

France


What are the applications of cauchy-riemann equations in engineering?

Well, cauchy-riemann differential equation is a part of complex variables and in real-life applications such as engineering, it can be used in determining the flow of fluids, such as the flow around the pipe. In fluid mechanics, the cauchy-riemann equations are decribed by two complex variables, i.e. u and v, and if these two variables satisfy the equations in an open subset of R2, then the vector field can be asserted from the two cauchy-riemann equations, ux = vy (1) uy = - vx (2) This I think can help interpreting the potential flow (Wikipedia) in two dimensions using the cauchy-riemann equations. In fluid mechanics, the potential flow can be analyzed using the cauchy-riemann equations.


When can skewness be undefined?

Skewness can be undefined in cases where the data distribution lacks a defined mean or variance, such as in certain distributions that are not well-defined or have infinite variance. For example, a Cauchy distribution has undefined mean and variance, leading to undefined skewness. Additionally, skewness can also be undefined for discrete distributions with no variation, where all values are identical, resulting in a lack of dispersion.