Evaluation of areal versus point rainfall with sparse data

1981 ◽  
Vol 8 (2) ◽  
pp. 173-178 ◽  
Author(s):  
Van-Thanh-Van Nguyen ◽  
Jean Rousselle ◽  
M. B. McPherson
Keyword(s):  
Fixed Point ◽  
Distribution Function ◽  
Exponential Distribution ◽  
Correction Factor ◽  
Return Period ◽  
Specific Area ◽  
Sparse Data ◽  
Exceedance Probability ◽  
Fixed Area

A theoretical methodology is proposed to establish a relationship between the rainfall at a fixed point and the associated mean rainfall over a geographically fixed area. The distribution relation for mean rainfall over a specific area was derived using an exponential distribution function for hourly point rainfall. Values of the areal correction factor were estimated at equal levels of exceedance probability for point and areal mean rainfalls. Contrary to previous indications for a moving point, it was found that the areal correction factor for a fixed point and fixed area was not always equal to or less than unity. Furthermore, the areal correction factor was found to vary with the return period.

scholarly journals Scaling Characteristics of Storm-Centered ARF Using Radar Rainfall

10.29007/hmzf ◽  
2018 ◽  
Author(s):  
Eunji Kim ◽  
Boosik Kang
Keyword(s):  
Return Period ◽  
Reduction Factor ◽  
Exceedance Probability ◽  
Storm Events ◽  
Reference Area ◽  
Radar Rainfall ◽  
Areal Reduction Factor ◽  
Fixed Area ◽  
Spatio Temporal ◽  
Areal Rainfall

In the hydraulic design practices, it is necessary to apply areal reduction factor to convert the point rainfall into the areal rainfall in the reference area. The fixed-area ARF (ARFf), which is commonly used, can be considered unrealistic because it is estimated through independent frequency analysis of the point rainfall and the areal rainfall. In this study, storm-centred ARF (ARFs) was estimated using radar rainfall data to reflect the spatial distribution characteristics of storm events effectively. ARFs representing the duration and the return period was extracted by 95% non-exceedance probability of the Weibull distribution to derive envelope covering all values from various storm events. ARFs has a correlation with not only the reference area but also the duration and the return period. Their relationships are defined as the scaling factors. A new ARFs equation that reflects the spatio-temporal characteristics of actual rainfall is presented.

The Approximation of Sum of Independent Distributions by the Erlang Distribution Function

2002 ◽  
Vol 7 (1) ◽  
pp. 55-60 ◽  
Author(s):  
Antanas Karoblis
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Queueing Theory ◽  
Erlang Distribution ◽  
Estimation Of Error

The exponential distribution and the Erlang distribution function are been used in numerous areas of mathematics, and specifically in the queueing theory. Such and similar applications emphasize the importance of estimation of error of approximation by the Erlang distribution function. The article gives an analysis and technique of error’s estimation of an accuracy of such approximation, especially in some specific cases.

STOCHASTIC TRANSMISSION DYNAMICS OF COVID-19 WITHIN A DENSITY DEPENDENT POPULATION

10.33003/659 ◽  
2021 ◽  
Vol 5 (2) ◽  
pp. 567-573
Author(s):  
Lubem M. Kwaghkor ◽  
Stephen E. Onah ◽  
Ibrahim G. Basi ◽  
Theophilus Danjuma
Keyword(s):  
Distribution Function ◽  
Exponential Distribution ◽  
Severe Disease ◽  
The Elderly ◽  
Control Measures ◽  
Special Treatment ◽  
Susceptible Population ◽  
Density Dependent ◽  
Infected People ◽  
Population Sizes

Coronavirus diseases (COVID-19) is a respiratory disease. Most infected people are known to develop mild to moderate symptoms and recover without requiring special treatment except for those who have underlying medical conditions and the elderly have a higher risk of developing severe disease. This research is aimed at studying the probable spread of the COVID-19 virus within a completely susceptible density-dependent population using a modified exponential distribution function. The modified exponential distribution function was extended to include the Basic Reproduction Number which was computed using the Nigerian COVID-19 index cases from 27th February to 18th April, 2020 to be. Various interesting results were obtained for the including the time period for the spread for different population sizes. The duration of the spread of the virus is from 4 to 7 hours with an average of 5.5 hours. This indicates that, for one infectious person with  to enter a completely susceptible population of size , the virus can spread through the entire population in about  hours if no control measures are in place.

Characterizations of the exponential distribution by order statistics

1974 ◽  
Vol 11 (03) ◽  
pp. 605-608 ◽  
Author(s):  
J. S. Huang
Keyword(s):  
Distribution Function ◽  
Order Statistics ◽  
Exponential Distribution ◽  
Special Cases ◽  
Characterization Theorems

Let X 1,n ≦ … ≦ Xn, n be the order statistics of a sample of size n from a distribution function F. Desu (1971) showed that if for all n ≧ 2, nX 1,n is identically distributed as X 1, 1, then F is the exponential distribution (or else F degenerates). The purpose of this note is to point out that special cases of known characterization theorems already constitute an improvement over this result. We show that the characterization is preserved if “identically distributed” is weakened to “having identical (finite) expectation”, and “for all n ≧ 2” is weakened to “for a sequence of n's with divergent sum of reciprocals”.

scholarly journals Space–Time Characteristics of Areal Reduction Factors and Rainfall Processes

2020 ◽  
Vol 21 (4) ◽  
pp. 671-689 ◽  
Author(s):  
Korbinian Breinl ◽  
Hannes Müller-Thomy ◽  
Günter Blöschl
Keyword(s):  
Return Period ◽  
Lightning Activity ◽  
Convective Activity ◽  
Convective Rainfall ◽  
The West ◽  
Rain Gauges ◽  
Fixed Area ◽  
Relationship Of ◽  
The Relationship ◽  
Reduction Factors

AbstractWe estimate areal reduction factors (ARFs; the ratio of catchment rainfall and point rainfall) varying in space and time using a fixed-area method for Austria and link them to the dominating rainfall processes in the region. We particularly focus on two subregions in the west and east of the country, where stratiform and convective rainfall processes dominate, respectively. ARFs are estimated using a rainfall dataset of 306 rain gauges with hourly resolution for five durations between 1 h and 1 day. Results indicate that the ARFs decay faster with area in regions of increased convective activity than in regions dominated by stratiform processes. Low ARF values occur where and when lightning activity (as a proxy for convective activity) is high, but some areas with reduced lightning activity exhibit also rather low ARFs as, in summer, convective rainfall can occur in any part of the country. ARFs tend to decrease with increasing return period, possibly because the contribution of convective rainfall is higher. The results of this study are consistent with similar studies in humid climates and provide new insights regarding the relationship of ARFs and dominating rainfall processes.

scholarly journals The Characteristic Function Property of Mixture Negative Binomial-Exponential Distribution

2018 ◽  
Vol 3 (4) ◽  
pp. 178
Author(s):  
Dodi Devianto ◽  
Sarah Sarah ◽  
Siska Dwi Kumala ◽  
Maiyastri Maiyastri
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Characteristic Function ◽  
Exponential Distribution ◽  
Negative Binomial Distribution ◽  
Probability Distribution Function ◽  
Negative Binomial ◽  
Stieltjes Transform ◽  
Function Property ◽  
New Distribution

This paper introduces a new distribution by mixing the negative binomial distribution and exponential distribution namely negative binomial-exponential (NB-E) distribution. In is given the probability distribution function of NB-E distribution and its characteristic function by using Fourier-Stieltjes transform. In addition we present the some properties of characteristic function from NB-E distribution.

scholarly journals Multivariate hydrologic design methods under nonstationary conditions and application to engineering practice

2019 ◽  
Vol 23 (3) ◽  
pp. 1683-1704 ◽  
Author(s):  
Cong Jiang ◽  
Lihua Xiong ◽  
Lei Yan ◽  
Jianfan Dong ◽  
Chong-Yu Xu
Keyword(s):  
Return Period ◽  
Flood Event ◽  
Exceedance Probability ◽  
Dependence Structure ◽  
Engineering Practice ◽  
Time Varying ◽  
Marginal Distributions ◽  
Hydrologic Design ◽  
The Given ◽  
Nonstationary Conditions

Abstract. Multivariate hydrologic design under stationary conditions is traditionally performed through the use of the design criterion of the return period, which is theoretically equal to the average inter-arrival time of flood events divided by the exceedance probability of the design flood event. Under nonstationary conditions, the exceedance probability of a given multivariate flood event varies over time. This suggests that the traditional return-period concept cannot apply to engineering practice under nonstationary conditions, since by such a definition, a given multivariate flood event would correspond to a time-varying return period. In this paper, average annual reliability (AAR) was employed as the criterion for multivariate design rather than the return period to ensure that a given multivariate flood event corresponded to a unique design level under nonstationary conditions. The multivariate hydrologic design conditioned on the given AAR was estimated from the nonstationary multivariate flood distribution constructed by a dynamic C-vine copula, allowing for time-varying marginal distributions and a time-varying dependence structure. Both the most-likely design event and confidence interval for the multivariate hydrologic design conditioned on the given AAR were identified to provide supporting information for designers. The multivariate flood series from the Xijiang River, China, were chosen as a case study. The results indicated that both the marginal distributions and dependence structure of the multivariate flood series were nonstationary due to the driving forces of urbanization and reservoir regulation. The nonstationarities of both the marginal distributions and dependence structure were found to affect the outcome of the multivariate hydrologic design.

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