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BOD test bottles at the laboratory of a wastewater treatment plant. Biochemical oxygen demand (also known as BOD or biological oxygen demand) is an analytical parameter representing the amount of dissolved oxygen (DO) consumed by aerobic bacteria growing on the organic material present in a water sample at a specific temperature over a specific time period.
Important special cases of the order statistics are the minimum and maximum value of a sample, and (with some qualifications discussed below) the sample median and other sample quantiles. When using probability theory to analyze order statistics of random samples from a continuous distribution , the cumulative distribution function is used to ...
Many governments impose strict regulations regarding the maximum chemical oxygen demand allowed in wastewater before it can be returned to the environment. For example, in Switzerland , a maximum oxygen demand between 200 and 1000 mg/L must be reached before wastewater or industrial water can be returned to the environment [2] .
The sample maximum and minimum are the least robust statistics: they are maximally sensitive to outliers.. This can either be an advantage or a drawback: if extreme values are real (not measurement errors), and of real consequence, as in applications of extreme value theory such as building dikes or financial loss, then outliers (as reflected in sample extrema) are important.
Instead a load profile can be inferred from customer billing or other data. An example of a practical calculation used by utilities is using a transformer's maximum demand reading and taking into account the known number of each customer type supplied by these transformers. This process is called load research.
There is a paucity of reliable guidance on estimating sample sizes before starting the research, with a range of suggestions given. [ 16 ] [ 19 ] [ 20 ] [ 21 ] In an effort to introduce some structure to the sample size determination process in qualitative research, a tool analogous to quantitative power calculations has been proposed.
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data.This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable.
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic.If an arbitrarily large number of samples, each involving multiple observations (data points), were separately used in order to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample, then the sampling ...