Bent cable regression of normally distributed data: applied to the fifth Covid-19 wave in Egypt

Abstract EN

The bent-cable model is used to describe the fifth Covid-19 wave in Egypt The data are normally distributed but rightly skewed The model comprises two linear segments, joined smoothly by a quadratic bend.

The class of bent cables includes, as a limiting case, the popular piecewise-linear model (with a sharp kink), otherwise known as the broken stick.

Associated with bent-cable regression is the estimation of the bend width parameter, through which the abruptness of the underlying transition may be assessed.

We present worked the recorded fifth Covid-19 Wave in Egypt to demonstrate the regularity and irregularity of bent-cable regression encountered in finite-sample settings.

We also presented a new method to determine the two inflection points by drawing a line from the CTP to the lowest point in each side of the curve, the points of intersection between the drawn lines and the real data will be the points of inflection.

The validity of the suggested method is validated.

Under such conditions, the least-squares estimators are shown (i) to be consistent, and (ii) to asymptotically follow a multivariate normal distribution.

Hence the least-squares estimators are used to analysis the considered data