scholarly journals Tests of Fit for the Logarithmic Distribution

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
D. J. Best ◽  
J. C. W. Rayner ◽  
O. Thas
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Probability Generating Function ◽  
Smooth Tests ◽  
The Third ◽  
Chi Squared ◽  
Logarithmic Distribution ◽  
Anderson Darling ◽  
Tests Of Fit ◽  
Integrated Distribution Function

Smooth tests for the logarithmic distribution are compared with three tests: the first is a test due to Epps and is based on a probability generating function, the second is the Anderson-Darling test, and the third is due to Klar and is based on the empirical integrated distribution function. These tests all have substantially better power than the traditional Pearson-Fisher X2 test of fit for the logarithmic. These traditional chi-squared tests are the only logarithmic tests of fit commonly applied by ecologists and other scientists.

scholarly journals Distribution Function, Probability Generating Function and Archimedean Generator

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2108
Author(s):  
Weaam Alhadlaq ◽  
Abdulhamid Alzaid
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Generating Functions ◽  
Probability Generating Function ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Archimedean Copulas ◽  
Cumulative Distribution Functions ◽  
Probability Generating Functions ◽  
Real Functions

Archimedean copulas form a very wide subclass of symmetric copulas. Most of the popular copulas are members of the Archimedean copulas. These copulas are obtained using real functions known as Archimedean generators. In this paper, we observe that under certain conditions the cumulative distribution functions on (0, 1) and probability generating functions can be used as Archimedean generators. It is shown that most of the well-known Archimedean copulas can be generated using such distributions. Further, we introduced new Archimedean copulas.

On the MX/G/∞ queue by heterogeneous customers in a batch

1994 ◽  
Vol 31 (01) ◽  
pp. 280-286
Author(s):  
Tang Dac Cong
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Service Time ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Fixed Time ◽  
General Distribution ◽  
Different Types ◽  
Number Of Customers ◽  
Collective Marks

We consider the Mx/G/∞ queue in which customers in a batch belong to k different types, and a customer of type i requires a non-negative service time with general distribution function Bi (s) (1 ≦ i ≦ k). The number of customers in a batch is stochastic. The joint probability generating function of the number of customers of type i being served at a fixed time t > 0 is derived by the method of collective marks.

On the MX/G/∞ queue by heterogeneous customers in a batch

1994 ◽  
Vol 31 (1) ◽  
pp. 280-286 ◽  
Author(s):  
Tang Dac Cong
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Service Time ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Fixed Time ◽  
General Distribution ◽  
Different Types ◽  
Number Of Customers ◽  
Collective Marks

We consider the Mx/G/∞ queue in which customers in a batch belong to k different types, and a customer of type i requires a non-negative service time with general distribution function Bi(s) (1 ≦ i ≦ k). The number of customers in a batch is stochastic. The joint probability generating function of the number of customers of type i being served at a fixed time t > 0 is derived by the method of collective marks.

scholarly journals Smooth Tests of Fit for the Lindley Distribution

Stats ◽  
2018 ◽  
Vol 1 (1) ◽  
pp. 92-97
Author(s):  
D. Best ◽  
J. Rayner
Keyword(s):  
Exponential Distribution ◽  
Lindley Distribution ◽  
Smooth Tests ◽  
Smooth Test ◽  
Anderson Darling ◽  
Tests Of Fit

We consider the little-known one parameter Lindley distribution. This distribution may be of interest as it appears to be more flexible than the exponential distribution, the Lindley fitting more data than the exponential. We give smooth tests of fit for this distribution. The smooth test for the Lindley has power comparable with the Anderson-Darling test. Advantages of the smooth test are discussed. Examples that illustrate the flexibility of this distributions is given.

Functional normalizations for the branching process with infinite mean

1979 ◽  
Vol 16 (03) ◽  
pp. 513-525 ◽  
Author(s):  
Andrew D. Barbour ◽  
H.-J. Schuh
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Branching Process ◽  
Analogous Result ◽  
Sufficient Conditions ◽  
Probability Generating Function ◽  
Random Variables ◽  
Watson Process

It is well known that, in a Bienaymé-Galton–Watson process (Zn ) with 1 < m = EZ 1 < ∞ and EZ 1 log Z 1 <∞, the sequence of random variables Znm –n converges a.s. to a non–degenerate limit. When m =∞, an analogous result holds: for any 0< α < 1, it is possible to find functions U such that α n U (Zn ) converges a.s. to a non-degenerate limit. In this paper, some sufficient conditions, expressed in terms of the probability generating function of Z 1 and of its distribution function, are given under which a particular pair (α, U) is appropriate for (Zn ). The most stringent set of conditions reduces, when U (x) x, to the requirements EZ 1 = 1/α, EZ 1 log Z 1 <∞.

scholarly journals EVALUATION OF THE BEST-FIT PROBABILITY OF DISTRIBUTION AND RETURN PERIODS OF RIVER DISCHARGE PEAKS. CASE STUDY: AWETU RIVER, JIMMA, ETHIOPIA

2019 ◽  
Vol 4 (4) ◽  
pp. 361-368 ◽  
Author(s):  
Tolera Abdisa Feyissa ◽  
Nasir Gebi Tukura
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Peak Discharge ◽  
Environmental Damage ◽  
Return Periods ◽  
Chi Squared ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal ◽  
Best Fit

The identification of the best distribution function is essential to estimate a river peak discharge or magnitude of river floods for management of watershed and ecosystems. However, inadequate estimation of the river peak discharge and floods magnitude may decrease the efficiency of water-resources management, resulting in soil erosion, landslides, environmental damage and ecosystem degradation. To overcome this problem in hydrology, different methods have been employed, applying a probability distribution.In this study to determine the suitable probability of distribution for estimating the annual discharge series with different return periods, the annual mean and peak discharges of the Awetu River (Jimma, Ethiopia) over a 24 years’ time period have been collected and used. After the homogeneity and consistency test, data were analyzed to predict extreme values and were applied in seven different probability distribution functions by using L-moment and easy fit methods. Then, three goodness of fit tests, Anderson-Darling (AD), Kolmogorov-Smirnov (KS), and Chi-Squared (x2) tests, were used to select the best probability distribution function for the study area. The obtained results indicate that, Log-normal distribution function is the best-fit distribution to estimate the peak discharge recurrence of the Awetu River. The 5-year, 10-year, 25-year, 50-year, 100-year and 1000-year return periods of discharge were calculated for this river. The results of this study are useful for the development of more accurate models of flooding inundation and hazard analysis. AVALIAÇÃO DA MELHOR PROBABILIDADE DE AJUSTE DE DISTRIBUIÇÃO E PERÍODOS DE RETORNO DOS PICOS DE DESCARGA FLUVIAL. ESTUDO DE CASO: AWETU RIVER, JIMMA, ETIÓPIAResumoAvaliação da melhor função de probabilidade de distribuição e de períodos de retorno de picos de descarga de rio. Estudo de caso: Rio Awetu, Jimma, Etiópia. A identificação da melhor função de distribuição é essencial para estimar um pico de descarga de rios ou a magnitude das inundações de bacias hidrográficas e ecossistemas, tendo em vista a gestão dos sistemas hídricos e dos ecossistemas. Entretanto, uma estimativa inadequada da magnitude do pico de vazão e inundações do rio pode diminuir a eficiência do gerenciamento dos recursos hídricos, resultando em erosão do solo, deslizamentos de terra, danos ambientais e degradação do ecossistema. Para superar esse problema na hidrologia, diferentes métodos foram empregados, aplicando funções de probabilidade de distribuição e retorno.Neste estudo, para determinar a probabilidade adequada de distribuição e para estimar séries de descarga anuais com diferentes períodos de retorno, foram usados dados de médias anuais de picos de descarga do Rio Awetu (Jimma, Etiópia) durante um período de 24 anos. Após o teste de homogeneidade e consistência, os dados foram analisados para prever valores extremos e foram aplicados a sete funções diferentes de probabilidade de distribuição, usando o momento L e métodos de ajuste fácil. Em seguida foram utilizados, três testes de qualidade de ajuste, Anderson-Darling (AD), Kolmogorov-Smirnov (KS), and Chi-Squared (x2), para selecionar a melhor função de probabilidade de distribuição para a área de estudo. Os resultados obtidos indicam que, a função de distribuição log-normal é a que mais se adequa para estimar a recorrência de picos de descarga do Rio Awetu. Os períodos de retorno de descarga de 5 anos, 10 anos, 25 anos, 50 anos, 100 anos e 1000 anos foram calculados para este rio. Os resultados deste estudo são úteis para o desenvolvimento de modelos mais precisos de inundação e análise de risco.Palavras-chave: Descarga de Rio. Qualidade de ajuste. Log Pearson Tipo III. Distribuição de probabilidade. 

Functional normalizations for the branching process with infinite mean

1979 ◽  
Vol 16 (3) ◽  
pp. 513-525 ◽  
Author(s):  
Andrew D. Barbour ◽  
H.-J. Schuh
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Branching Process ◽  
Analogous Result ◽  
Sufficient Conditions ◽  
Probability Generating Function ◽  
Random Variables ◽  
Watson Process

It is well known that, in a Bienaymé-Galton–Watson process (Zn) with 1 < m = EZ1 < ∞ and EZ1 log Z1 <∞, the sequence of random variables Znm –n converges a.s. to a non–degenerate limit. When m =∞, an analogous result holds: for any 0< α < 1, it is possible to find functions U such that α n U (Zn) converges a.s. to a non-degenerate limit. In this paper, some sufficient conditions, expressed in terms of the probability generating function of Z1 and of its distribution function, are given under which a particular pair (α, U) is appropriate for (Zn). The most stringent set of conditions reduces, when U (x) x, to the requirements EZ1 = 1/α, EZ1 log Z1 <∞.

On the absorption probabilities and mean time for absorption for discrete Markov chains

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Nikolaos Halidias
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Markov Chains ◽  
Generating Function ◽  
Discrete Time ◽  
Probability Generating Function ◽  
The Mean ◽  
Mean Time ◽  
Absorption Probabilities

Abstract In this note we study the probability and the mean time for absorption for discrete time Markov chains. In particular, we are interested in estimating the mean time for absorption when absorption is not certain and connect it with some other known results. Computing a suitable probability generating function, we are able to estimate the mean time for absorption when absorption is not certain giving some applications concerning the random walk. Furthermore, we investigate the probability for a Markov chain to reach a set A before reach B generalizing this result for a sequence of sets A 1 , A 2 , … , A k {A_{1},A_{2},\dots,A_{k}} .

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