Modelling the entire range of daily precipitation using phase-type distributions

Rho, Hyunwoo; Kim, Joseph H.T.

doi:10.1016/j.advwatres.2018.11.014

“…Hydrological studies on daily rainfall data typically focus only on the positive part of the semicontinuous distribution (Rho and Kim (2019)) and set the probability of observing a zero to the proportion of zeros in the data. For example, Papalexiou and Koutsoyiannis (2012) have focused on the MaxEnt solution of the continuous part alone and explored various distributions including a generalized gamma distribution, generalized beta distribution etc with applications for the daily rainfall data.…”

Section: H(γ)mentioning

confidence: 99%

“…Density estimation by entropy maximization is widely used in hydrology. In hydrological studies, semi-continuous data is typically modelled by ignoring the point mass at zero and focusing exclusively on the positive continuous part (Rho and Kim (2019)). This is true for density estimation using entropy maximization as well.…”

Section: Introductionmentioning

confidence: 99%

Density estimation using entropy maximization for semi-continuous data

Popuri¹,

Neerchal

²

,

Mehta

³

et al. 2021

Digital Signal Processing

2

0

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Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel algorithm to estimate the density function for semi-continuous data using the principle of maximum entropy. Unlike existing methods in the literature, our algorithm needs only the sample values of the constraint functions in the entropy maximization problem and does not need the entire sample. Using simulations, we show that the estimate of the entropy produced by our algorithm has significantly less bias compared to existing methods. An application to the daily rainfall data is provided.

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“…Hydrological studies on daily rainfall data typically focus only on the positive part of the semicontinuous distribution (Rho and Kim (2019)) and set the probability of observing a zero to the proportion of zeros in the data. For example, Papalexiou and Koutsoyiannis (2012) have focused on the MaxEnt solution of the continuous part alone and explored various distributions including a generalized gamma distribution, generalized beta distribution etc with applications for the daily rainfall data.…”

Section: An Alternating Entropy Maximization Algorithm For Semi-conti...mentioning

confidence: 99%

Density Estimation using Entropy Maximization for Semi-continuous Data

Popuri¹,

Neerchal²,

Mehta³

et al. 2020

Preprint

0

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Semi-continuous data comes from a distribution that is a mixture of the point mass at zero and a continuous distribution with support on the positive real line. A clear example is the daily rainfall data. In this paper, we present a novel algorithm to estimate the density function for semi-continuous data using the principle of maximum entropy. Unlike existing methods in the literature, our algorithm needs only the sample values of the constraint functions in the entropy maximization problem and does not need the entire sample. Using simulations, we show that the estimate of the entropy produced by our algorithm has significantly less bias compared to existing methods. An application to the daily rainfall data is provided.

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“…In recent years, studies have shown that meteorological elements, such as temperature and precipitation, have a long-term statistical memory. The occurrence time of extreme events has a significant long-term correlation, and it is related to the clustering of extreme events [13][14][15]. Fisher et al [16] reported that the frequencies of extreme events are independent of each other and follow a Poisson distribution.…”

Section: Introductionmentioning

confidence: 99%

Self-Organized Criticality of Precipitation in the Rainy Season in East China

Qian

¹

,

Xiao

²

,

Wang

³

et al. 2022

Atmosphere

0

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Based on daily precipitation data from 1960 to 2017 in the rainy season in east China, to a given percentile threshold of one observation station, the time that precipitation spends below threshold is defined as quiet time τ. The probability density functions τ in different thresholds follow power-law distributions with exponent β of approximately 1.2 in the day, pentad and ten-day period time scales, respectively. The probability density functions τ in different regions follow the same rules, too. Compared with sandpile model, Γ function describing the collapse behavior can effectively scale the quiet time distribution of precipitation events. These results confirm the assumption that for observation station data and low-resolution precipitation data, even in China, affected by complex weather and climate systems, precipitation is still a real world example of self-organized criticality in synoptic. Moreover, exponent βof the probability density function τ, mean quiet time τ¯q and hazard function Hq of quiet times can give sensitive regions of precipitation events in China. Usual intensity precipitation events (UPEs) easily occur and cluster mainly in the middle Yangtze River basin, east of the Sichuan Province and north of the Gansu Province. Extreme intensity precipitation events (EPEs) more easily occur in northern China in the rainy season. UPEs in the Hubei Province and the Hunan Province are more likely to occur in the future. EPEs in the eastern Sichuan Province, the Guizhou Province, the Guangxi Province and Northeast China are more likely to occur.

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Modelling the entire range of daily precipitation using phase-type distributions

Cited by 6 publications

References 22 publications

Density estimation using entropy maximization for semi-continuous data

Density estimation using entropy maximization for semi-continuous data

Density Estimation using Entropy Maximization for Semi-continuous Data

Self-Organized Criticality of Precipitation in the Rainy Season in East China

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