Comparison of stochastic models of rainfall processes in mountainous climatic conditions

2010 ◽  
Vol 1 (2) ◽  
pp. 135-146
Author(s):  
J. Y. Lee ◽  
M. Y. Han ◽  
D. K. Kim ◽  
W. H. Ji
Keyword(s):  
Exponential Distribution ◽  
Gamma Distribution ◽  
Rainwater Harvesting ◽  
Daily Rainfall ◽  
Percentage Error ◽  
Parameter Distribution ◽  
Mountainous Region ◽  
Simpler Algorithm ◽  
Two Parameter ◽  
Mixed Exponential Distribution

The main objective of this work was to find a stochastic simulation model that was suitable for designing a rainwater harvesting system for agricultural water utilization and irrigation water in a mountainous region. Several models were applied using daily rainfall data from two sites (Gangneung and Daekwanreung) to assess the accuracy and suitability of the model for simulating the daily rainfall. The amount of rainfall for the mountainous region was well described by a two-parameter gamma distribution and performed better than other distributions. However, validation tests revealed that the annual mean absolute percentage error (MAPE) was more than 10% at both locations. This result was different from some previous research in which a three-parameter mixed-exponential distribution was well described. In addition, although the exponential distribution was also well described by a second-order expression, the use of a one-parameter distribution had a simpler algorithm than the two-parameter gamma distribution and the three-parameter mixed-exponential distribution.

scholarly journals One-Parameter Weibull-Type Distribution, Its Relative Entropy with Respect to Weibull and a Fractional Two-Parameter Exponential Distribution

Stats ◽  
2019 ◽  
Vol 2 (1) ◽  
pp. 34-54
Author(s):  
Aris Alexopoulos
Keyword(s):  
Exponential Distribution ◽  
Relative Entropy ◽  
Real Data ◽  
Parameter Distribution ◽  
Sample Mean ◽  
Type Distribution ◽  
Two Parameter ◽  
New Distribution ◽  
Extra Parameter ◽  
Mathematical Characteristics

A new one-parameter distribution is presented with similar mathematical characteristics to the two parameter conventional Weibull. It has an estimator that only depends on the sample mean. The relative entropy with respect to the Weibull distribution is derived in order to examine the level of similarity between them. The performance of the new distribution is compared to the Weibull and in some cases the Gamma distribution using real data. In addition, the Exponential distribution is modified to include an extra parameter via a simple transformation using fractional mathematics. It will be shown that the modified version also exhibits Weibull characteristics for particular values of the second parameter.

scholarly journals A Comparative Study on the Derivation of Unit Hydrograph for Dhadhar River Basin

2019 ◽  
pp. 36-43
Author(s):  
Prerna Sutariya
Keyword(s):  
River Basin ◽  
Gamma Distribution ◽  
Beta Distribution ◽  
Daily Rainfall ◽  
Distribution Functions ◽  
Unit Hydrograph ◽  
Model Study ◽  
Hourly Rainfall ◽  
The One ◽  
Two Parameter

Several techniques are available for the development of the unit hydrograph. But most of these traditional methods require manual fitting of the unit hydrograph through few points, which does not guarantee the area under the unit hydrograph to be unity. More over most of the stations are ungauged, due to which it becomes difficult to develop the unit hydrograph. So in order to overcome these problems, two methods have been considered in this study for the development of the unit hydrograph for Dhadhar river basin. They are the “two parameter Gamma distribution” and “three parameter Beta distribution”, both of which are based on Probability Distribution Functions (pdfs). The unit hydrograph developed by the two parameter Gamma distribution match well with the one developed by CWC method, but the unit hydrograph developed by the three parameter Beta distribution does not match well with the one developed by the CWC method. From the unit hydrograph, runoff hydrograph is convoluted for the year 2018. For this the hourly rainfall are generated from daily rainfall values by disaggregation. But on plotting, the simulated discharge hydrograph is found to be greater than the observed discharge. This may be due to non-incorporation of the inflow outflow processes of many hydraulic structures such as dams, irrigation schemes etc., existing in the basin in the model study.

scholarly journals A New Goodness-of-Fit Test for the Two-Parameter Gamma Distribution

2022 ◽  
Vol 3 (1) ◽  
pp. 01-06
Author(s):  
Mbanefo S. Madukaife
Keyword(s):  
Gamma Distribution ◽  
Goodness Of Fit ◽  
Critical Values ◽  
Parameter Distribution ◽  
Goodness Of Fit Test ◽  
Gamma Distributions ◽  
Two Parameter

This paper proposes a new goodness-of-fit for the two-parameter distribution. It is based on a function of squared distances between empirical and theoretical quantiles of a set of observations being hypothesized to have come from the gamma distribution. The critical values of the proposed statistic are evaluated through extensive simulations of the unit-scaled gamma distributions and computations. The empirical powers of the statistic are obtained and compared with some well-known tests for the gamma distribution, and the results show that the proposed statistic can be recommended as a test for the gamma distribution.

scholarly journals A Case Study on Reliability, Water Demand and Economic Analysis of Rainwater Harvesting in Australian Capital Cities

Water ◽  
2021 ◽  
Vol 13 (19) ◽  
pp. 2606
Author(s):  
Preeti Preeti ◽  
Ataur Rahman
Keyword(s):  
Economic Analysis ◽  
Water Demand ◽  
Rainwater Harvesting ◽  
Daily Rainfall ◽  
Cost Ratio ◽  
Capital Cities ◽  
Australian Capital ◽  
Benefit Cost Ratio ◽  
Roof Area ◽  
Daily Water

This paper presents reliability, water demand and economic analysis of rainwater harvesting (RWH) systems for eight Australian capital cities (Adelaide, Brisbane, Canberra, Darwin, Hobart, Melbourne, Perth and Sydney). A Python-based tool is developed based on a daily water balance modelling approach, which uses input data such as daily rainfall, roof area, overflow losses, daily water demand and first flush. Ten different tank volumes are considered (1, 3, 5, 10, 15, 20, 30, 50, 75 and 100 m3). It is found that for a large roof area and tank size, the reliability of RWH systems for toilet and laundry use is high, in the range of 80–100%. However, the reliability for irrigation use is highly variable across all the locations. For combined use, Adelaide shows the smallest reliability (38–49%), while Hobart demonstrates the highest reliability (61–77%). Furthermore, economic analysis demonstrates that in a few cases, benefit–cost ratio values greater than one can be achieved for the RWH systems. The findings of this study will help the Australian Federal Government to enhance RWH policy, programs and subsidy levels considering climate-sensitive inputs in the respective cities.

One-Sided β-Content Tolerance Factors forthe Two Parameter Exponential Distribution

Technometrics ◽  
1976 ◽  
Vol 18 (3) ◽  
pp. 333-340 ◽  
Author(s):  
William C. Guenther ◽  
S. A. Patil ◽  
V. R.R. Uppuluri
Keyword(s):  
Exponential Distribution ◽  
Tolerance Factors ◽  
Two Parameter
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