ARRIVAL PATTERNS AND TRAFFIC FLOW CHARACTERISTICS AT SIGNALIZED INTERSECTIONS

2021 ◽  
Vol 15 (1) ◽  
pp. 11-28
Author(s):  
Olanrewaju Oluwafemi Akinfala ◽  
Emmanuel Enyeribe Ege ◽  
Ladi Folorunso Ogunwolu
Keyword(s):  
Time Resolution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Model Misspecification ◽  
Flow Characteristics ◽  
P Value ◽  
High Time Resolution ◽  
P Values ◽  
Binomial Distributions ◽  
Density Analysis

Traffic arrivals at signal intersection approaches is inherently stochastic. This variability is typically reflected by I-ratio and there is a general consensus that the presence or absence of nearby upstream signal affects Variance to Mean Ratio (I-ratio). However, the effect of time resolution on arrival variability and the interaction effect between upstream signal and time resolution is yet to be examined in detail. This can lead to model misspecification and invariably, erroneous outcomes. This work examines the effect of time resolution and intersection type and their interaction on I-ratio and the resultant probability distributions. Traffic arrivals were measured at high time resolution- 10 seconds interval and then aggregated to lower time resolutions (30-150 seconds) at six intersections. Spectral density analysis showed statistically significant periodicity, specifically at 30 seconds interval with p-values < 0.0001 at all connected intersections while observations at isolated intersections lacked periodicity. Two-way ANOVA using I-ratio as the dependent variable and intersection type and time-resolution as the independent variables was performed. Statistically significant effect with F-value 8.606 at p-value < 0.0001 and R2 value 0.32 were observed. Intersection type, time resolution and the interaction between them were statistically significant, with p-values 0.002, < 0.0001 and 0.000 respectively. The combined effect of these factors led to a wide I-ratio range of 0.37-9.2. Negative Binomial, Poisson, and Binomial distributions represented 76.4, 20.4 and 4.2% of all I-ratios observed. Therefore, in contrast to literature which recommends Poisson, Negative Binomial may be a better suited probability distribution for traffic arrivals.

scholarly journals A Generalised Exponential-Lindley Mixture of Poisson Distribution

2019 ◽  
Vol 3 ◽  
pp. 11-20
Author(s):  
Binod Kumar Sah ◽  
A. Mishra
Keyword(s):  
Poisson Distribution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Mixture Distribution ◽  
Discrete Data ◽  
Likelihood Method ◽  
P Value ◽  
Data Set ◽  
Lindley Distribution ◽  
First Four Moments

Background: The exponential and the Lindley (1958) distributions occupy central places among the class of continuous probability distributions and play important roles in statistical theory. A Generalised Exponential-Lindley Distribution (GELD) was given by Mishra and Sah (2015) of which, both the exponential and the Lindley distributions are the particular cases. Mixtures of distributions form an important class of distributions in the domain of probability distributions. A mixture distribution arises when some or all the parameters in a probability function vary according to certain probability law. In this paper, a Generalised Exponential- Lindley Mixture of Poisson Distribution (GELMPD) has been obtained by mixing Poisson distribution with the GELD. Materials and Methods: It is based on the concept of the generalisations of some continuous mixtures of Poisson distribution. Results: The Probability mass of function of generalized exponential-Lindley mixture of Poisson distribution has been obtained by mixing Poisson distribution with GELD. The first four moments about origin of this distribution have been obtained. The estimation of its parameters has been discussed using method of moments and also as maximum likelihood method. This distribution has been fitted to a number of discrete data-sets which are negative binomial in nature and it has been observed that the distribution gives a better fit than the Poisson–Lindley Distribution (PLD) of Sankaran (1970). Conclusion: P-value of the GELMPD is found greater than that in case of PLD. Hence, it is expected to be a better alternative to the PLD of Sankaran for similar type of discrete data-set which is negative binomial in nature.

scholarly journals An Error Model for Uncertainty Quantification in High-Time-Resolution Precipitation Products

2014 ◽  
Vol 15 (3) ◽  
pp. 1274-1292 ◽  
Author(s):  
Viviana Maggioni ◽  
Mathew R. P. Sapiano ◽  
Robert F. Adler ◽  
Yudong Tian ◽  
George J. Huffman
Keyword(s):  
Time Resolution ◽  
Probability Distributions ◽  
Total Error ◽  
Tropical Rainfall Measuring Mission ◽  
Satellite Observation ◽  
High Time ◽  
High Time Resolution ◽  
Validation Data ◽  
The Difference ◽  
Climate Prediction Center

Abstract This study proposes a new framework, Precipitation Uncertainties for Satellite Hydrology (PUSH), to provide time-varying, global estimates of errors for high-time-resolution, multisatellite precipitation products using a technique calibrated with high-quality validation data. Errors are estimated for the widely used Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis (TMPA) 3B42 product at daily/0.25° resolution, using the NOAA Climate Prediction Center (CPC) Unified gauge dataset as the benchmark. PUSH estimates the probability distribution of reference precipitation given the satellite observation, from which the error can be computed as the difference (or ratio) between the satellite product and the estimated reference. The framework proposes different modeling approaches for each combination of rain and no-rain cases: correct no-precipitation detection (both satellite and gauges measure no precipitation), missed precipitation (satellite records a zero, but the gauges detect precipitation), false alarm (satellite detects precipitation, but the reference is zero), and hit (both satellite and gauges detect precipitation). Each case is explored and explicitly modeled to create a unified approach that combines all four scenarios. Results show that the estimated probability distributions are able to reproduce the probability density functions of the benchmark precipitation, in terms of both expected values and quantiles of the distribution. The spatial pattern of the error is also adequately reproduced by PUSH, and good agreement between observed and estimated errors is observed. The model is also able to capture missed precipitation and false detection uncertainties, whose contribution to the total error can be significant. The resulting error estimates could be attached to the corresponding high-resolution satellite precipitation products.

Recent results on characterization of probability distributions: a unified approach through extensions of Deny&s theorem

1986 ◽  
Vol 18 (03) ◽  
pp. 660-678 ◽  
Author(s):  
C. Radhakrishna Rao ◽  
D. N. Shanbhag
Keyword(s):  
Negative Binomial ◽  
Short Proof ◽  
Probability Distributions ◽  
Direct Link ◽  
Unified Approach ◽  
Binomial Distributions ◽  
Characterization Of Probability Distributions ◽  
Special Cases ◽  
Convolution Equations

The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny (1960) and Deny (1961). Recently, Lau and Rao (1982) have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla (1975) and a lemma of Shanbhag (1977). The extended versions of Deny&amp;s theorem contained in the papers by Lau and Rao, and Shanbhag (which we refer to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. In this paper we review some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. We also give a short proof of Lau–Rao theorem based on Deny&amp;s theorem and thus establish a direct link between the results of Deny (1961) and those of Lau and Rao (1982). A variant of Lau–Rao theorem is proved and applied to some characterization problems.

Standard distributions in R.

2021 ◽  
pp. 335-347
Author(s):  
Donald L. J. Quicke ◽  
Buntika A. Butcher ◽  
Rachel A. Kruft Welton
Keyword(s):  
Programming Language ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Test Statistics ◽  
P Values ◽  
Chi Squared ◽  
Student’S T ◽  
Log Normal

Abstract There are a number of in-built probability distributions, including uniform, binomial, negative binomial, normal, log-normal, logistic, exponential, Chisquared, Poisson, gamma, Fisher's F, Student's t, Weibull and others. These are used to generate p-values from test statistics, to generate random values from a distribution or to generate expected distributions. This chapter deals with standard distributions in R (a programming language that has a huge range of inbuilt statistical and graphical functions), focusing on the normal, Student's t, lognormal, logistic, Poisson, gamma, and the Chi-squared.

scholarly journals Best constants for tensor products of Bernstein, Szász and Baskakov operators

2000 ◽  
Vol 62 (2) ◽  
pp. 211-220 ◽  
Author(s):  
Jesús de la Cal ◽  
Ana M. Valle
Keyword(s):  
Tensor Product ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Best Constants ◽  
Moduli Of Continuity ◽  
Lower And Upper Bounds ◽  
Baskakov Operators ◽  
Binomial Distributions ◽  
Families Of Operators ◽  
Crucial Ingredient

We consider tensor product operators and discuss their best constants in preservation inequalities concerning the usual moduli of continuity. In a previous paper, we obtained lower and upper bounds on such constants, under fairly general assumptions on the operators. Here, we concentrate on the l∞-modulus of continuity and three celebrated families of operators. For the tensor product of k identical copies of the Bernstein operator Bn, we show that the best uniform constant coincides with the dimension k when k ≥ 3, while, in case k = 2, it lies in the interval [2, 5/2] but depends upon n. Similar results also hold when Bn is replaced by a univariate Szász or Baskakov operator. The three proofs follow the same pattern, a crucial ingredient being some special properties of the probability distributions involved in the mentioned operators, namely: the binomial, Poisson, and negative binomial distributions.

Recent results on characterization of probability distributions: a unified approach through extensions of Deny&s theorem

1986 ◽  
Vol 18 (3) ◽  
pp. 660-678 ◽  
Author(s):  
C. Radhakrishna Rao ◽  
D. N. Shanbhag
Keyword(s):  
Negative Binomial ◽  
Short Proof ◽  
Probability Distributions ◽  
Direct Link ◽  
Unified Approach ◽  
Binomial Distributions ◽  
Characterization Of Probability Distributions ◽  
Special Cases ◽  
Convolution Equations

The problem of identifying solutions of general convolution equations relative to a group has been studied in two classical papers by Choquet and Deny (1960) and Deny (1961). Recently, Lau and Rao (1982) have considered the analogous problem relative to a certain semigroup of the real line, which extends the results of Marsaglia and Tubilla (1975) and a lemma of Shanbhag (1977). The extended versions of Deny&s theorem contained in the papers by Lau and Rao, and Shanbhag (which we refer to as LRS theorems) yield as special cases improved versions of several characterizations of exponential, Weibull, stable, Pareto, geometric, Poisson and negative binomial distributions obtained by various authors during the last few years. In this paper we review some of the recent contributions to characterization of probability distributions (whose authors do not seem to be aware of LRS theorems or special cases existing earlier) and show how improved versions of these results follow as immediate corollaries to LRS theorems. We also give a short proof of Lau–Rao theorem based on Deny&s theorem and thus establish a direct link between the results of Deny (1961) and those of Lau and Rao (1982). A variant of Lau–Rao theorem is proved and applied to some characterization problems.

scholarly journals Bounds for some entropies and special functions

2018 ◽  
Vol 34 (1) ◽  
pp. 09-15
Author(s):  
ADINA BARAR ◽  
◽  
GABRIELA RALUCA MOCANU ◽  
IOAN RASA ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Convex Function ◽  
Negative Binomial ◽  
Special Functions ◽  
Probability Distributions ◽  
Real Parameter ◽  
Binomial Distributions

We consider a family of probability distributions depending on a real parameter and including the binomial, Poisson and negative binomial distributions. The corresponding index of coincidence satisfies a Heun differential equation and is a logarithmically convex function. Combining these facts we get bounds for the index of coincidence, and consequently for Renyi and Tsallis entropies of order 2.

Standard distributions in R.

2021 ◽  
pp. 335-347
Author(s):  
Donald L. J. Quicke ◽  
Buntika A. Butcher ◽  
Rachel A. Kruft Welton
Keyword(s):  
Programming Language ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Test Statistics ◽  
P Values ◽  
Chi Squared ◽  
Student’S T ◽  
Log Normal

Abstract There are a number of in-built probability distributions, including uniform, binomial, negative binomial, normal, log-normal, logistic, exponential, Chisquared, Poisson, gamma, Fisher's F, Student's t, Weibull and others. These are used to generate p-values from test statistics, to generate random values from a distribution or to generate expected distributions. This chapter deals with standard distributions in R (a programming language that has a huge range of inbuilt statistical and graphical functions), focusing on the normal, Student's t, lognormal, logistic, Poisson, gamma, and the Chi-squared.

Assessment of Susceptibility Risk Factors for ADHD in Imaging Genetic Studies

2016 ◽  
Vol 23 (7) ◽  
pp. 671-681 ◽  
Author(s):  
N. Vilor-Tejedor ◽  
S. Alemany ◽  
J. Forns ◽  
A. Cáceres ◽  
M. Murcia ◽  
...  
Keyword(s):  
Risk Factors ◽  
Statistical Power ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Significant Risk ◽  
P Value ◽  
Adhd Symptoms ◽  
Genetic Studies ◽  
Dichotomous Outcome ◽  
Independent Population

Objective: ADHD consists of a count of symptoms that often presents heterogeneity due to overdispersion and excess of zeros. Statistical inference is usually based on a dichotomous outcome that is underpowered. The main goal of this study was to determine a suited probability distribution to analyze ADHD symptoms in Imaging Genetic studies. Method: We used two independent population samples of children to evaluate the consistency of the standard probability distributions based on count data for describing ADHD symptoms. Results: We showed that the zero-inflated negative binomial (ZINB) distribution provided the best power for modeling ADHD symptoms. ZINB reveals a genetic variant, rs273342 (Microtubule-Associated Protein [MAPRE2]), associated with ADHD ( p value = 2.73E-05). This variant was also associated with perivascular volumes (Virchow–Robin spaces; p values < 1E-03). No associations were found when using dichotomous definition. Conclusion: We suggest that an appropriate modeling of ADHD symptoms increases statistical power to establish significant risk factors.

On characterization of certain probability distributions

1972 ◽  
Vol 71 (2) ◽  
pp. 347-352 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Distribution Function ◽  
Linear Regression ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Random Variable ◽  
The Other ◽  
Linear Statistic ◽  
Binomial Distributions ◽  
Independent Observations

Introduction: Let X1, X2, …, Xn be n (n ≤ 2) independent observations on a random variable X with distribution function F. Also let L = L (X1, X2, …, Xn) be a linear statistic and Q = Q (X1, X2, …, Xn) be a homogeneous quadratic statistic. In this paper, we consider the problem of characterizing a class of probability distributions by the linear regression of the statistic Q on the other statistic L. In section 2, we obtain a characterization of a class of probability distributions, which includes the normal and the Poisson distributions. In section 3, a class of distributions including the gamma, the binomial and the negative binomial distributions is characterized.

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