scholarly journals Baseline Methods for Bayesian Inference in Gumbel Distribution

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1267
Author(s):  
Jacinto Martín ◽  
María Isabel Parra ◽  
Mario Martínez Pizarro ◽  
Eva L. Sanjuán
Keyword(s):  
Gumbel Distribution ◽  
Extreme Value ◽  
Estimation Methods ◽  
Extreme Value Distributions ◽  
Distribution Method ◽  
New Methods ◽  
Initial Idea ◽  
Block Maxima ◽  
Extreme Distribution ◽  
Baseline Values

Usual estimation methods for the parameters of extreme value distributions only employ a small part of the observation values. When block maxima values are considered, many data are discarded, and therefore a lot of information is wasted. We develop a model to seize the whole data available in an extreme value framework. The key is to take advantage of the existing relation between the baseline parameters and the parameters of the block maxima distribution. We propose two methods to perform Bayesian estimation. Baseline distribution method (BDM) consists in computing estimations for the baseline parameters with all the data, and then making a transformation to compute estimations for the block maxima parameters. Improved baseline method (IBDM) is a refinement of the initial idea, with the aim of assigning more importance to the block maxima data than to the baseline values, performed by applying BDM to develop an improved prior distribution. We compare empirically these new methods with the Standard Bayesian analysis with non-informative prior, considering three baseline distributions that lead to a Gumbel extreme distribution, namely Gumbel, Exponential and Normal, by a broad simulation study.

An Extreme Value Model for U.S. Hail Size

2017 ◽  
Vol 145 (11) ◽  
pp. 4501-4519 ◽  
Author(s):  
John T. Allen ◽  
Michael K. Tippett ◽  
Yasir Kaheil ◽  
Adam H. Sobel ◽  
Chiara Lepore ◽  
...  
Keyword(s):  
Gumbel Distribution ◽  
The United States ◽  
Value Theory ◽  
Extreme Value ◽  
Extreme Value Distributions ◽  
The Past ◽  
Return Levels ◽  
Data Limitations ◽  
Extreme Value Model ◽  
Value Model

The spatial distribution of return intervals for U.S. hail size is explored within the framework of extreme value theory using observations from the period 1979–2013. The center of the continent has experienced hail in excess of 5 in. (127 mm) during the past 30 yr, whereas hail in excess of 1 in. (25 mm) is more common in other regions, including the West Coast. Observed hail sizes show heavy quantization toward fixed-diameter reference objects and are influenced by spatial and temporal biases similar to those noted for hail occurrence. Recorded hail diameters have been growing in recent decades because of improved reporting. These data limitations motivate exploration of extreme value distributions to represent the return periods for various hail diameters. The parameters of a Gumbel distribution are fit to dithered observed annual maxima on a national 1° × 1° grid at locations with sufficient records. Gridded and kernel-smoothed return sizes and quantiles up to the 200-yr return period are determined for the fitted Gumbel distribution. These results are used to illustrate return levels for hail greater than a given size for at least one location within each 1° × 1° grid box for the United States.

scholarly journals Application of Frequency Analysis on Peak River Discharge toward the Cumulative Floatable Litter Load at Log Boom Sungai Batu

2019 ◽  
Vol 266 ◽  
pp. 02002
Author(s):  
Nur Khaliesah Abdul Malik ◽  
Nor Rohaizah Jamil ◽  
Latifah Abd Manaf ◽  
Mohd Hafiz Rosli ◽  
Zulfa Hanan Ash’aari ◽  
...  
Keyword(s):  
Frequency Analysis ◽  
Return Period ◽  
River Discharge ◽  
Linear Regression Analysis ◽  
Gumbel Distribution ◽  
Environmental Issues ◽  
Decision Making Process ◽  
Rapid Urbanization ◽  
Distribution Method ◽  
Period 2

The accumulation of floatable litter in the river is mainly influenced by the increasing number of human population, rapid urbanization and development which indirectly lead to the changes of hydrological processes in river discharge, decreasing the water quality and aesthetical value of the river. The main objective of this paper is to determine the cumulative floatable litter load captured at the log boom during the extreme events by using the Gumbel distribution method for frequency analysis in river discharge of Sungai Batu. The annual maximum river discharge for a period of 35 years (1982 to 2016) was used in Gumbel distribution method to obtain the discharge for different return period (2, 5, 10, 25, 50, 100, and 200). The result shows that the estimated discharge (103.17 m³/s) can estimate the cumulative floatable litter load (53267.27 kg/day) at 50 years return period. The R2 value obtained from non – linear regression analysis is 0.9986 indicate that Gumbel distribution is suitable to predict the expected discharge of the river. This study is very crucial for the related agencies in highlighting this environmental issues for their future references which can be used as a guidelines during the decision making process in making better improvement.

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