Frequency Distributions for Coliform Bacteria in Water

Abstract

An examination of the frequency distributions most commonly used to estimate mean coliform densities in flowing water compares their reliability in describing coliform data obtained from sample tests.

Agreement, Precision, and Accuracy of Epifluorescence Microscopy Methods for Enumeration of Total Bacterial Numbers

“…By varying filtration conditions, we could demonstrate that Poisson, normal, and log-normal distributions can be obtained sometimes, while NB distribution could be fitted for most cell count distributions (see the supplemental material). NB distributions are often found among bacterial counts in various scales, including repeated measurements and spatial or temporal distribution of specific bacteria (14,19,26,47), which correspond to distributions of ␣ i or ␥ ijk in the model of equation 1. A published case of NB distribution of bacterial cells in a microscope scale, i.e., the scale of ε ijkl in equation 1, can be found in counts of ingested bacteria within nanoflagellate cells (11).…”

The response of fecal coliforms and antibiotic‐resistantEscherichia colito incremental doses of ozone during disinfection of activated sludge effluent

“…Furthermore, temporal variation of coliform density has been reported as lognormally distributed (33). Consequently, log N/log N Q , the log removal fraction, seems to better represent the reduction of bacteria in wastewater.…”

Drinking Water Microbiology

“…Therefore, the value of the parameter k of the negative binomial distribution, which can range between 0 and plus infinity, can be considered a measure of bacterial heterogeneity in the water system: as k approaches infinity the negative binomial distribution simplifies to the Poisson and, inversely, the smaller the value of k the greater the bacterial heterogeneity of the system. The negative binomial distribution has been shown to give a good fit to many actual bacterial frequency distributions and is widely used to represent bacterial counts from water samples collected over time and/or space EI-Shaarawi et al, 1985;Maul et al, 1985a,b;Muenz, 1978;Pipes et al, 1977;Thomas, 1955). The parameters of the probability distribution are then used to summarize the information in the data and to assist in designing future data collections for monitoring the bacteriological water quality (EI-Shaarawi et al, 1985;Esterby, 1982;Maul et al, 1985b;Pipes and Christian, 1982).…”

“…Pipes et al (1977) reported that examination of replicates of a single sample of water as well as sets of samples of a water taken over a short time period generally formed a frequency distribution more consistent with the negative binomial or log-normal than with the Poisson. In a more extensive study of water distribution samples obtained over a period of time, similar conclusions were reached .…”