Exact distribution of the peak streamflow

Nadarajah, Saralees

doi:10.1029/2006wr005300

Cited by 8 publications

(5 citation statements)

References 10 publications

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“…These curves are very useful in several fields. For a given probability π, they are defined by B(π) = m1(q)/(πµ 1 ′ ) and L(π) = m1(q)/ µ 1 ′ , respectively, where m1(q) comes from (18) with r = 1 and q = Q(π) is evaluated from (16).…”

Section: Incomplete Momentsmentioning

confidence: 99%

An Extended Fr echet Distribution: Properties and Applications

Mansoor¹,

Tahir²,

Alzaatreh³

et al. 2021

Journal of Data Science

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In this paper, we introduce an extended four-parameter Fr´echet model called the exponentiated exponential Fr´echet distribution, which arises from the quantile function of the standard exponential distribution. Various of its mathematical properties are derived including the quantile function, ordinary and incomplete moments, Bonferroni and Lorenz curves, mean deviations, mean residual life, mean waiting time, generating function, Shannon entropy and order statistics. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The usefulness of the new distribution is illustrated by means of three real lifetime data sets. In fact, the new model provides a better fit to these data than the Marshall-Olkin Fr´echet, exponentiated-Fr´echet and Fr´echet models.

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Section: Incomplete Momentsmentioning

confidence: 99%

An Extended Fr echet Distribution: Properties and Applications

Mansoor¹,

Tahir²,

Alzaatreh³

et al. 2021

Journal of Data Science

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“…Lognormal and gamma families are selected as alternatives for representing the probability distribution of monthly river flow. Both of them have been frequently used for river flow simulation [ Sangal and Biswas , ; Fernandez and Salas , ; Nadarajah , ]. Three copula families, i.e., Clayton, survival Clayton, and Gaussian, are chosen as options to capture the serial dependence.…”

Section: Model Definitionmentioning

confidence: 99%

“…Redefining

boldY

as a random vector of flows of two adjacent months, i.e.,

Y = true[Y_{t - 1}, Y_{t} true]

(in the boundary season,

Y_{t - 1}

denotes the flow in December of the previous year, and

Y_{t}

represents that in January of the current year), this paper primarily attempts to model the joint density

ϕ true(y_{t - 1}, y_{t} | x true)

conditioned on covariate information

boldx

. Right‐skewed distributions with positive support, such as lognormal and gamma distributions, are deemed as plausible choices for representing monthly river flow [ Sangal and Biswas , ; Fernandez and Salas , ; Nadarajah , ]. The dependence structure of adjacent flows is captured using copulas [ Joe , ; Nelsen , ; Lee and Salas , ].…”

Section: Introductionmentioning

confidence: 99%

Monthly river flow simulation with a joint conditional density estimation network

Singh

Mishra

2013

Water Resour. Res.

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River flow synthesizing and downscaling are required for the analysis of risks associated with water resources management plans and for regional impact studies of climate change. This paper presents a probabilistic model that synthesizes and downscales monthly river flow by estimating the joint distribution of flows of two adjacent months conditional on covariates. The covariates may consist of lagged and aggregated flow variables (synthesizing), exogenous climatic variables (downscaling), or combinations of these two types. The joint distribution is constructed by connecting two marginal distributions in terms of copulas. The relationship between covariates and distribution parameters is approximated by an artificial neural network, which is calibrated using the principle of maximum likelihood. Outputs of the neural network yield parameters of the joint distribution. From the estimated joint distribution, a conditional distribution of river flow of current month given the estimation of the previous month can be derived. Depending on the different types of covariate information, this conditional distribution may serve as the “engine” for synthesizing or downscaling river flow sequences. The idea of the proposed model is illustrated using three case studies. The first case deals with synthetic data and shows that the model is capable of fitting a nonstationary joint distribution. Second, the model is utilized to synthesize monthly river flow at four sample stations on the main stream of the Colorado River. Results reveal that the model reproduces essential evaluation statistics fairly well. Third, a simple illustrative example for river flow downscaling is presented. Analysis indicates that the model can be a viable option to downscale monthly river flow as well.

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“…Nadarajah and Kotz (2005), and Nadarajah (2007) used also this result to obtain the properties of the distribution of the difference between two independent Gumbel variates, and to Iacbellis and Fiorentino (2000), and Fiorentino et al (2006)'s model for peak streamflow.…”

Section: Generating Functionmentioning

confidence: 99%

“…Since it is the most attractive generalization of the exponential distribution, the GE model has received increased attention and many authors have studied its various properties and also proposed comparisons with other distributions. Some significant references are: Gupta and Kundu (2001a;2001b;2003;2004;2007;2008;, Kundu et al (2005), Nadarajah and Kotz (2006), Dey and Kundu (2009), Pakyari (2010) and . In fact, the GE model has been proven to be a good alternative to the gamma, Weibull and log-normal distributions, all of them with two-parameters.…”

Section: Approach 1: Adding One Shape Parametermentioning

confidence: 99%

The odd generalized exponential family of distributions with applications

et al. 2015

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We propose a new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub. It includes as a special case the widely known exponentiated-Weibull distribution. We present and discuss three special models in the family. Its density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order statistics. For the first time, we obtain the generating function of the Fréchet distribution. Two useful characterizations of the family are also proposed. The parameters of the new family are estimated by the method of maximum likelihood. Its usefulness is illustrated by means of two real lifetime data sets.

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Exact distribution of the peak streamflow

Cited by 8 publications

References 10 publications

An Extended Fr echet Distribution: Properties and Applications

An Extended Fr echet Distribution: Properties and Applications

Monthly river flow simulation with a joint conditional density estimation network

The odd generalized exponential family of distributions with applications

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