On the Berry-Esséen bound of frequency polygons for ϕ-mixing samples

When the fitness of a trait is influenced by how common it is (i.e., its frequency) relative to different traits within a population, this is referred to as frequency-dependent selection. Frequency-dependent selection may occur between species or within a single species. This type of selection can either be positive—with more common phenotypes having higher fitness—or negative, with rarer phenotypes conferring increased fitness.

Concrete mixing ensures a homogenous blend where aggregates are well-coated with cement paste. Concrete mixing is typically done using two main types of mixers: batch and continuous. Batch mixers handle one batch at a time, thoroughly combining materials before discharging and receiving the next batch. In contrast, continuous mixers receive a steady flow of ingredients, mixing them consistently and discharging without interruption. Within batch mixers, tilting drum mixers mix with internal...

The concept of mixing time is significant in producing a uniform concrete mix with the required strength. The mixing period starts once all components are in the mixer. Initially, the mixer is charged with 10% of the water, followed by the consistent addition of solids and then 80% of the water. The remaining water is added later, within the first quarter of the mixing period. The minimum mixing time varies according to the mixer's capacity; for example, mixers with up to 1 cubic yard...

Ready-mixed concrete, also known as pre-mixed concrete, is prepared in a centralized plant and then transported in trucks to construction sites where it is ready for placement. This type of concrete is categorized into central-mixed, truck-mixed (or transit-mixed), and shrink-mixed. Central-mixed concrete is entirely prepared at a plant and moved to the site in agitator trucks that rotate at a speed of 2 to 6 rpm. Truck-mixed concrete, on the other hand, has the ingredients batched at the plant...

A frequency is the number of times a value of the data occurs. The sum of all the frequency values represents the total number of students included in the sample. It is commonly used to group data of quantitative types. Frequency distributions can be displayed in a table, histogram, line graph, dot plot, or pie chart, just to name a few. A histogram is a graphical representation of tabulated frequencies, shown as adjacent rectangles, erected over discrete intervals (bins), with an area equal to...

Sometimes, data gathered from an experiment on a large sample or population are organized into concise tables. In such cases, the frequency of the quantitative data set is plotted in the form of a table. Or else, the data values are grouped into the quantity’s intervals, which form classes, and their respective frequencies are known. That is, the data values are distributed over different categories or classes. This is known as frequency distribution.
When such a data set is encountered,...