Correction: Topp-Leone Cauchy Family of Distributions with Applications in Industrial Engineering

Correction: Journal of Statistical Theory and Applications (2023) 22:339–365 https://doi.org/10.1007/s44199-023-00066-4

In the original article, there was a mistake in formula (7). Instead of:

$$ F(x;\,\nu ) = \left[ {1 - \left( {\frac{1}{2} - \frac{1}{\pi }\arctan \frac{P(x;\,\tau ) - b}{a}} \right)^{2} } \right]^{\alpha } $$

$\nu = (\alpha ,a,b,\tau )$ and $\alpha ,a,\tau > 0$, it should be:

$$ F(x;\,\nu ) = \left\{ {1 - \left[ {\frac{1}{2} - \frac{1}{\pi }\arctan \left( {\frac{x(P(x;\,\tau ) + m) - b}{a}} \right)} \right]^{2} } \right\}^{\alpha } $$

$\nu = (\alpha ,a,b,\tau ,m)$ and $\alpha ,a,\tau ,m > 0$ and $x \in\, ] - \infty ; + \infty [.$

This slightly affects the developments of the properties in the Sect. 2, A special member: the TLCAR distribution. The authors state that this correction does not change the sense of the results reported in their paper and its conclusion. The authors are grateful to Professor Hamedani Gholamhossein for his help improving this paper.