Confidence limits for the mean of exponential distribution in any time-sequential samples

2005 ◽  
Vol 48 (9) ◽  
pp. 1182 ◽  
Author(s):  
Jiading CHEN
Keyword(s):  
Exponential Distribution ◽  
Confidence Limits ◽  
Sequential Samples ◽  
The Mean

Quantification of small-scale heterogeneity in aquatic aminopeptidase activity

2020 ◽  
Vol 84 ◽  
pp. 127-140
Author(s):  
BM Gaas ◽  
JW Ammerman
Keyword(s):  
Chlorophyll Fluorescence ◽  
Leucine Aminopeptidase ◽  
Hudson River ◽  
Aminopeptidase Activity ◽  
Small Scale ◽  
Analysis Instrument ◽  
Sequential Samples ◽  
Degree Of Confidence ◽  
The Mean ◽  
Hydrolysis Of

Leucine aminopeptidase (LAP) is one of the enzymes involved in the hydrolysis of peptides, and is sometimes used to indicate potential nitrogen limitation in microbes. Small-scale variability has the potential to confound interpretation of underlying patterns in LAP activity in time or space. An automated flow-injection analysis instrument was used to address the small-scale variability of LAP activity within contiguous regions of the Hudson River plume (New Jersey, USA). LAP activity had a coefficient of variation (CV) of ca. 0.5 with occasional values above 1.0. The mean CVs for other biological parameters—chlorophyll fluorescence and nitrate concentration—were similar, and were much lower for salinity. LAP activity changed by an average of 35 nmol l-1 h-1 at different salinities, and variations in LAP activity were higher crossing region boundaries than within a region. Differences in LAP activity were ±100 nmol l-1 h-1 between sequential samples spaced <10 m apart. Variogram analysis indicated an inherent spatial variability of 52 nmol l-1 h-1 throughout the study area. Large changes in LAP activity were often associated with small changes in salinity and chlorophyll fluorescence, and were sensitive to the sampling frequency. This study concludes that LAP measurements in a sample could realistically be expected to range from zero to twice the average, and changes between areas or times should be at least 2-fold to have some degree of confidence that apparent patterns (or lack thereof) in activity are real.

scholarly journals A Bimodal Extension of the Exponential Distribution with Applications in Risk Theory

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 679
Author(s):  
Jimmy Reyes ◽  
Emilio Gómez-Déniz ◽  
Héctor W. Gómez ◽  
Enrique Calderín-Ojeda
Keyword(s):  
Exponential Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Estimation Methods ◽  
Inverse Gaussian ◽  
New Family ◽  
Tail Distribution ◽  
Zero Values ◽  
The Mean ◽  
Positive Support

There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.

The Influence of Training Phase on Error of Measurement in Jump Performance

2016 ◽  
Vol 11 (2) ◽  
pp. 235-239 ◽  
Author(s):  
Kristie-Lee Taylor ◽  
Will G. Hopkins ◽  
Dale W. Chapman ◽  
John B. Cronin
Keyword(s):  
Mixed Model ◽  
Training Phase ◽  
Confidence Limits ◽  
Mean Power ◽  
Random Factor ◽  
Jump Performance ◽  
Mean Error ◽  
Overload Training ◽  
The Mean ◽  
Error Of Measurement

The purpose of this study was to calculate the coefficients of variation in jump performance for individual participants in multiple trials over time to determine the extent to which there are real differences in the error of measurement between participants. The effect of training phase on measurement error was also investigated. Six subjects participated in a resistance-training intervention for 12 wk with mean power from a countermovement jump measured 6 d/wk. Using a mixed-model meta-analysis, differences between subjects, within-subject changes between training phases, and the mean error values during different phases of training were examined. Small, substantial factor differences of 1.11 were observed between subjects; however, the finding was unclear based on the width of the confidence limits. The mean error was clearly higher during overload training than baseline training, by a factor of ×/÷ 1.3 (confidence limits 1.0–1.6). The random factor representing the interaction between subjects and training phases revealed further substantial differences of ×/÷ 1.2 (1.1–1.3), indicating that on average, the error of measurement in some subjects changes more than in others when overload training is introduced. The results from this study provide the first indication that within-subject variability in performance is substantially different between training phases and, possibly, different between individuals. The implications of these findings for monitoring individuals and estimating sample size are discussed.

Synchrony of frond dynamics among patches of the clonal seaweed Mazzaella parksii (Rhodophyta) at local spatial scale

2004 ◽  
Vol 84 (5) ◽  
pp. 883-886 ◽  
Author(s):  
Ricardo Scrosati
Keyword(s):  
Spatial Scale ◽  
Seasonal Changes ◽  
Pacific Coast ◽  
Spatial Scales ◽  
Sampling Effort ◽  
Confidence Limits ◽  
Seasonal Trends ◽  
Intertidal Seaweed ◽  
The Mean

This study investigated the synchrony of frond dynamics among patches of the intertidal seaweed Mazzaella parksii (=M. cornucopiae; Rhodophyta: Gigartinales) at local spatial scale. At Prasiola Point (Pacific coast of Canada), the mean synchrony of the seasonal changes in frond density among seven permanent, 100-cm2 quadrats was significant (mean Pearson's r=0·73, with 0·65–0·81 as 95% confidence limits) between 1993 and 1995. This indicates that predicting seasonal trends for non-monitored patches at local spatial scale can be done relatively well based on observations on a limited number of quadrats. The identification of the spatial scales at which seaweed populations covary synchronously will permit minimizing sampling effort while retaining the ability to make valid predictions for non-monitored sites.

The influence of water temperature and pH on the survival of Fasciola hepatica miracidia

Parasitology ◽  
1984 ◽  
Vol 88 (1) ◽  
pp. 97-104 ◽  
Author(s):  
G. Smith ◽  
B. T. Grenfell
Keyword(s):  
Maximum Likelihood Method ◽  
Fasciola Hepatica ◽  
Good Description ◽  
Survival Function ◽  
Experimental Studies ◽  
Likelihood Method ◽  
Confidence Limits ◽  
Mean Values ◽  
Influence Of Water ◽  
The Mean

SUMMARYExperimental studies on the survival of Fasciola hepatica miracidia show no evidence that miracidial mortality varies with the pH of the medium, at least in the range 6·0–8·0. On the other hand, miracidial mortality is shown to vary with both the temperature of the medium and the age of the larvae. The mean expected life-span of the miracidium decreases from about 35 h at 6°C to about 6° h at 25° C. The Gompertz survival function provides a good description of the miracidial survivorship curves over the range of temperatures used, and we describe, a maximum likelihood method of estimating the mean values of the parameters of this function, together with their approximate 95% confidence limits.

Population dynamics and production of a brine shrimp, Parartemia zietziana Sayce (Crustacea : Anostraca), in two salt lakes in westren Victoria, Australia

1977 ◽  
Vol 28 (4) ◽  
pp. 417 ◽  
Author(s):  
R Marchant ◽  
WD Williams
Keyword(s):  
Population Dynamics ◽  
Population Density ◽  
Temperature Stress ◽  
Brine Shrimp ◽  
Dry Weight ◽  
Salt Lakes ◽  
Confidence Limits ◽  
Length Frequency ◽  
Population Densities ◽  
The Mean

Quantitative samples of P. zietziana were taken monthly for two years from Pink Lake and Lake Cundare. Shrimps were usually contagiously distributed. To reduce error, samples were stratified resulting in confidence limits of 40-50% for the mean population density. Despite this variability, stable trends emerged, and variation was not so great as to mask significant differences. Length-frequency analyses distinguished cohorts; a regression was established between length and dry weight, enabling growth to be estimated from samples. By combining growth with population densities in Allen curves, production was computed. In Pink Lake and Lake Cundare mean pro- duction was 11.3 and 1.0 g dry weight m-2 year-1 respectively. Generally there were two or three generations per year, but time and extent of recruitment were not predictable. Each generation suffered continuous mortality, the death of young shrimps accounting for most of the production. This mortality remains unexplained; there are no significant predators and salinity and temperature stress would occur only during summer.

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