Developing methods for identifying the inflection point of a convex/concave curve

Abstract

We are introducing two methods for revealing the true inflection point of data that contains or not error. The starting point is a set of geometrical properties that follow the existence of an inflection point p for a smooth function. These properties connect the concept of convexity/concavity before and after p respectively with three chords defined properly. Finally a set of experiments is presented for the class of sigmoid curves and for the third order polynomials.

Agonism between family groups of cooperative breeding smooth-coated otters (Lutrogale perspicillata)

“…In this descriptive study, we introduced various models and highlighted the similarities among them (Burnham et al, 2011). After this, the inflection points of the prediction curves of the selected models were calculated using function ese (Christopoulos, 2012, inflection package, https://cran.r-project.org/web/packages/inflection/vignettes/inflection.html).…”

Shrub density effects on the presence of an endangered lizard of the Carrizo Plain National Monument, California

“…Pearson's Product-Moment Correlation was used to determine the strength and directions of the relationship between shrub density and cover. An approximation of second derivative for the data points for the mean fitted use by shrub density curve was used to determine the inflection point of fit (Christopoulos, 2014).…”

Elucidating how the red imported fire ant (Solenopsis invicta) diffused spatiotemporally among different landscapes in north Taiwan, 2008–2015

“…The cumulative proportions of positive tubes between consecutive years at different distances were calculated. The extreme distance estimator method (Christopoulos, 2014) was used to determine the turning point of the cumulative proportion diagram as the critical dispersal distance of S. invicta. Here, the identified critical dispersal distance means the highest probability of the dispersal distance.…”