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As premissas comumente consideradas nos modelos de estoques - aderência da demanda no lead-time de suprimento à Distribuição Normal, média e desvio-padrão conhecidos e lead-time de suprimento discreto - são freqüentemente irrealistas e podem implicar substanciais distorções na gestão dos estoques de novos produtos, sobretudo nos custos totais e nos indicadores de nível de serviço. Considerando que as empresas simultaneamente estocam os novos produtos e aprendem ao longo do tempo sobre as características da distribuição da demanda no lead-time de suprimento, é desenvolvida nesse artigo a solução do modelo (Q,r) - tamanho de lote e ponto de pedido - para o caso da demanda e do lead-time de suprimento com Distribuição Uniforme. Por ser definida por meio de dois parâmetros mais intuitivos que a média e o desvio-padrão - máximo e mínimo - e representar situações em que qualquer resultado tem igual probabilidade de ocorrência, a premissa da Distribuição Uniforme pode constituir uma primeira abordagem prática para a gestão de estoques de novos produtos.The premises commonly adopted in inventory management models - adherence of lead-time demand to Normal Distribution, known average and standard deviations, and discrete lead time - are often unrealistic and can lead to considerable distortions in new product inventories, particularly insofar as total costs and service level indicators are concerned. Considering that companies stock new products while simultaneously learning about the characteristics of lead-time demand distribution, this paper proposes the solution to the (Q,r) - order quantity and reorder point - inventory model for uniform demand and lead-time. The premise of Uniform Distribution is defined by two parameters that are more intuitive than mean and standard deviation - maximum and minimum - and it can also be applied when a result shows the same probability of occurring. Therefore, its adoption may be the first practical approach for new product inventory management.

Plate heat exchangers (PHE s) have been acquired a considerable attention and have been popularly used for both single-phase and two-phase flows in the air-conditioning systems. During the study of the flow distribution of the PHE s , the two-phase flow distribution is analysed experimentally. However, since the observation of the internal flow field of the PHE is very difficult, Computational Fluid Dynamics (CFD) can be used to better predict the fluids flow field inside the plate heat exchanger. In this study, ANSYS FLUENT is used to model the flow field composed of the K050 chevron PHE to observe the two-phase flow and uneven flow distribution. Moreover, the effect of the distributor on the gas-liquid distribution in the multi-channels flow field is also evaluated. The major effort of this paper is to investigate the effect of the two-phase flow distribution in multi-channels PHE with and without an inflow distributor. For the multi-channels PHE without distributor, the simulation results show that the flow must operate at high Reynolds numbers to obtain better enhancement in the flow distribution. If the PHE operates under Reynolds number less than 1500, the vapor-liquid distribution is non-uniform. Furthermore, it is observed that when the inflow distributor is added, the two-phase flow distribution of the vapor phase improves significantly. However, the flow distribution of the liquid phase is better under low Reynolds numbers condition. In addition, it has been shown that as Reynolds number increases, the liquid flow distribution is not affected by the inflow distributor. [ABSTRACT FROM AUTHOR]

A temporal pre-shaped burst-mode hybrid fiber-bulk laser system was illustrated at a 10 kHz rate with a narrow spectral linewidth. A theoretical model was proposed to counteract the temporal profile distortion and compensate for the desired one, based on reverse process of amplification. For uniformly modulated injection, amplified shapes were recorded and investigated in series for their varied pulse duration, envelope width and amplification delay, respectively. The pre-shaped output effectively realized a uniform distribution on a time scale for both the burst envelope and pulse shape under the action of the established theoretical method. Compared with previous amplification delay methods, this model possesses the capacity to extend itself for applications in burst-mode shaping with variable parameters and characteristics. The maximum pulse energy was enlarged up to 9.68 mJ, 8.94 mJ and 6.57 mJ with a 300 ns pulse duration over envelope widths of 2 ms to 4 ms. Moreover, the time-averaged spectral bandwidths were measured and characterized with Lonrentz fits of 68.3 MHz, 67.2 MHz and 67.7 MHz when the pulse duration varied from 100 ns to 300 ns.

We develop new goodness of fit test for uniform distribution based on a conditional moment characterization. We study the asymptotic properties of the proposed test statistic. We also present a goodness of fit test for uniform distribution to incorporate the right censored observations and studied its properties. A Monte Carlo simulation study is carried out to evaluate the finite sample performance of the proposed tests. We illustrate the test procedures using real data sets., (© Korean Statistical Society 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.)

The concept of sequence stability generalizes the idea of uniform distribution. A sequence is p-stable if the set of residue frequencies of the sequence reduced modulo pr is eventually constant as a function of r. The authors identify and characterize the stability of second-order recurrences modulo odd primes.

In this survey, we use the normal linear model to demonstrate the use of the linear Bayes method. The superiorities of linear Bayes estimator (LBE) over the classical UMVUE and MLE are established in terms of the mean squared error matrix (MSEM) criterion. Compared with the usual Bayes estimator (obtained by the MCMC method) the proposed LBE is simple and easy to use with numerical results presented to illustrate its performance. We also examine the applications of linear Bayes method to some other distributions including two-parameter exponential family, uniform distribution and inverse Gaussian distribution, and finally make some remarks. [ABSTRACT FROM AUTHOR]

In this study, the probability‐guaranteed H∞ control of networked control systems (NCSs) with time‐varying networked‐induced delays is addressed. The time‐varying delays are modelled as polytopic uncertainty by a new approximation method based on real Jordan form. The system uncertainty lies in a parameter hyper‐rectangle box which can shrink, i.e. the probability can be less than one with a better disturbance attenuation level. By the uniformity principle and the one‐to‐one correspondence between the time delays and the vertices of polytopic system, a sufficient condition for the NCS to achieve prescribed performance with a given probability is derived. The controller synthesis problem is also proposed to meet the probabilistic requirement by solving a set of bilinear matrix inequalities iteratively. A uniform distribution is assumed for all the delays and thus the maximal probability guaranteeing the given performance can be calculated. [ABSTRACT FROM AUTHOR]

One standard way of considering a probability distribution on the unit n -cube, [ 0 , 1 ] n , due to Sklar (1959), is to decompose it into its marginal distributions and a copula, i.e. a probability distribution on [ 0 , 1 ] n with uniform marginals. The definition of copula was extended by Jones et al. (2014) to probability distributions on products of circles. This paper defines a copula as a probability distribution on a product of compact Riemannian manifolds that has uniform marginals. Basic properties of such copulae are established. Two fairly general constructions of copulae on products of compact homogeneous manifolds are given; one is based on convolution in the isometry group, the other using equivariant functions from compact Riemannian manifolds to their spaces of square integrable functions. Examples illustrate the use of copulae to analyse bivariate spherical data and bivariate rotational data. [ABSTRACT FROM AUTHOR]

We critically examine a number of flaws in the current procedure for the final draw of the FIFA World Cup™: imbalance (the eight groups are not of the same competitive level), unfairness (some teams have a greater chance than others of ending up in a tough group), and uneven distribution (all the possible outcomes of the draw are not equally likely). These flaws result from the way FIFA has decided to enforce the geographic constraints that they put on the draw. We explain how, by building eight pots by level organized in an S-curve, and drawing first a continental distribution of the groups and then the teams, we can enforce the geographic constraints without sacrificing balance, fairness, and even distribution. As a result, we describe a new tractable draw procedure that produces eight balanced and geographically diverse groups, is fair to all teams, and gives equally likely outcomes. [ABSTRACT FROM AUTHOR]

This study measures the long‐term electric energy data of an electric vehicle (EV) charging station, and uses these field measurements to analyse and construct the load behaviour model of an EV charging station. According to the statistics of field measurements, the state of charge of EV battery pack at the start of charging and the number of EVs starting charging in each time interval can be modelled using Poisson distribution, Roulette wheel selection and uniform distribution. The load behaviour of an EV charging station can be modelled and analysed accordingly. To validate the accuracy of the proposed load behaviour model, a portion of field measurements is reserved for load behaviour model verification. The proposed load behaviour model can also be used to analyse the impacts of EV charging stations on distribution systems. Test results show that the load behaviour model proposed in this study has higher accuracy and the impacts of EV charging stations on distribution systems can be analysed more effectively and precisely. [ABSTRACT FROM AUTHOR]

In order to research the effects of diversities of node movement on virus spreading in mobile Ad hoc networks (MANETs), this paper proposed a mobility model to construct a virus spreading model in MANETs based on cellular automata. It investigated not only the effects of diversities of node velocity, moving duration and staying duration but also the effects of direction range on virus spreading in MANETs. The simulations show that a smaller value of diversities of node movement implies a lower speed of virus spreading in MANETs. [ABSTRACT FROM AUTHOR]

Cuckoo search (CS), inspired by the obligate brood parasitic behavior of some cuckoo species, iteratively uses Lévy flights random walk (LFRW) and biased/selective random walk (BSRW) to search for new solutions. In this study, we seek a simple strategy to set the scaling factor in LFRW, which can vary the scaling factor to achieve better performance. However, choosing the best scaling factor for each problem is intractable. Thus, we propose a varied scaling factor (VSF) strategy that samples a value from the range [0,1] uniformly at random for each iteration. In addition, we integrate the VSF strategy into several advanced CS variants. Extensive experiments are conducted on three groups of benchmark functions including 18 common test functions, 25 functions proposed in CEC 2005, and 28 functions introduced in CEC 2013. Experimental results demonstrate the effectiveness of the VSF strategy. [ABSTRACT FROM AUTHOR]

The aim of this paper is to extend the concept of measure density introduced by Buck for finite unions of arithmetic progressions, to arbitrary subsets of $${\mathbb {N}}$$ defined by a given system of decompositions. This leads to a variety of new examples and to applications to uniform distribution theory. [ABSTRACT FROM AUTHOR]

This study investigates how the priority rankings for dam construction sites vary with multi-criteria decision making (MCDM) techniques and generation approaches for incomplete information. Strategic environmental assessment (SEA) seeks to recommend sustainable dam construction sites based on their environmental and ecological impacts in a long-term plan for dam construction (LPDC) in South Korea. However, if specific information is missing, the SEA is less useful for choosing a dam construction site. In this study, we applied AHP, ELECTRE III, PROMETHEE II and Compromise Programming as MCDM techniques, and used binomial and uniform distributions to generate missing information. We considered five dam site selection situations and compared the results as they depended on both MCDM techniques and information generation methods. The binomial generation method showed the most obvious priorities. All MCDM techniques showed similar priorities in the dam site selection results except for ELECTREE III. The results demonstrate that selecting an appropriate MCDM technique is more important than the data generation method. However, using binomial distribution to generate missing information is more effective in providing a robust priority than uniform distribution, which is a commonly used technique. [ABSTRACT FROM AUTHOR]

We explore in depth the number theoretic and statistical properties of certain sets of numbers arising from their Cantor series expansions. As a direct consequence of our main theorem we deduce numerous new results as well as strengthen the known ones. [ABSTRACT FROM AUTHOR]

Laser forming process is one of the newest methods of sheet metal bending which no mechanical force needs. Although lots of investigations on laser forming process of mono layer sheet metals have been done, any experiments have not been conducted around bi- layer sheets. In this paper, laser forming process of bi-layer Al/SiC work pieces under Gaussian and Uniform heat distribution has been studied. Elastic-plastic temperature dependent material properties are considered. Also, the boundary condition is applied as free heat convection. The results of numerical simulations revealed that the amount of bending angle in Uniform heat flux distribution is always further than Gaussian distribution. In addition, temperature distribution diagram in Uniform heat flux is almost 5% further than Gaussian form, and the maximum temperature in the work piece is 6% larger. For validation of numerical analyses, experimental tests are done by an Nd: YAG laser on bi-layer Fe/Al sheets. The amounts of bending angles are so close to the results of simulation. The average of the bending angle is almost derived 0.0038 Degree/ Watt in these experimental tests. [ABSTRACT FROM AUTHOR]

This paper reviews the number-theoretic concept of diaphony, a measure of uniform distribution for number sequences and point sets based on a Fourier theory approach, and its relation to crystallographic concepts like the largest interplanar spacing of a lattice, the structure-factor equation and the Patterson function. [ABSTRACT FROM AUTHOR]

Consider a theatre consisting of m rows each containing n seats. Theatregoers enter the theatre along aisles and pick a row which they enter along one of its two entrances so as to occupy a seat. Assume they select their seats uniformly and independently at random among the empty ones. A row of seats is narrow and an occupant who is already occupying a seat is blocking passage to new incoming theatregoers. As a consequence, occupying a specific seat depends on the courtesy of theatregoers and their willingness to get up so as to create free space that will allow passage to others. Thus, courtesy facilitates and may well increase the overall seat occupancy of the theatre. We say a theatregoer is courteous if (s)he will get up to let others pass. Otherwise, the theatregoer is selfish . A set of theatregoers is courteous with probability p (or p-courteous , for short) if each theatregoer in the set is courteous with probability p , randomly and independently. It is assumed that the behaviour of a theatregoer does not change during the occupancy of the row. Thus, p = 1 represents the case where all theatregoers are courteous and p = 0 when they are all selfish. In this paper, we are interested in the following question: what is the expected number of occupied seats as a function of the total number of seats in a theatre, n , and the probability that a theatregoer is courteous, p ? We study and analyze interesting variants of this problem reflecting behaviour of the theatregoers as entirely selfish, and p -courteous for a row of seats with one or two entrances and as a consequence for a theatre with m rows of seats with multiple aisles. We also consider the case where seats in a row are chosen according to the geometric distribution and the Zipf distribution (as opposed to the uniform distribution) and provide bounds on the occupancy of a row (and thus the theatre) in each case. Finally, we propose several open problems for other seating probability distributions and theatre seating arrangements. [ABSTRACT FROM AUTHOR]

We determine the joint limiting distribution of adjacent spacings around a central, intermediate, or an extreme order statistic $$X_{k:n}$$ of a random sample of size $$n$$ from a continuous distribution $$F$$ . For central and intermediate cases, normalized spacings in the left and right neighborhoods are asymptotically i.i.d. exponential random variables. The associated independent Poisson arrival processes are independent of $$X_{k:n}$$ . For an extreme $$X_{k:n}$$ , the asymptotic independence property of spacings fails for $$F$$ in the domain of attraction of Fréchet and Weibull ( $$\alpha \ne 1$$ ) distributions. This work also provides additional insight into the limiting distribution for the number of observations around $$X_{k:n}$$ for all three cases. [ABSTRACT FROM AUTHOR]

It is known that there is a constant c > 0 such that for every sequence x 1 , x 2 , … in [ 0 , 1 ) we have for the star discrepancy D N ∗ of the first N elements of the sequence that N D N ∗ ≥ c ⋅ log N holds for infinitely many N . Let c ∗ be the supremum of all such c with this property. We show c ∗ > 0.0646363 , thereby improving the until now known estimates. [ABSTRACT FROM AUTHOR]

LetX(1)≤X(2)≤···≤X(n)be the order statistics from independent and identically distributed random variables {Xi, 1≤i≤n} with a common absolutely continuous distribution function. In this work, first a new characterization of distributions based on order statistics is presented. Next, we review some conditional expectation properties of order statistics, which can be used to establish some equivalent forms for conditional expectations for sum of random variables based on order statistics. Using these equivalent forms, some known results can be extended immediately. [ABSTRACT FROM AUTHOR]

We derive a closed-form expression for the spatial fading correlation (SFC) between two arbitrary points in 3D-space for the uniform limited azimuth-elevation angle of arrival probability density function (pdf). This expression simplifies the computation of the SFC, can be used in any 3D antenna array geometry, and avoids the need to generate separate expressions for specific antenna array geometries. We corroborate the accuracy of the closed-form expression through application to 2D and 3D antenna array geometries. We expect the results presented in this letter to be of significant importance for performance evaluation and sensitivity analysis in multi-input multi-output (MIMO) systems. [ABSTRACT FROM PUBLISHER]

We consider a large class of fast growing sequences of numbers Un like the nth superfactorial , the nth hyperfactorial and similar ones. We show that their mantissas are distributed following Benford's law in the sense of the natural density. We prove that this is also verified by , by and is passed down to all the sequences obtained by iterating this design process. We also consider the superprimorial numbers and the products of logarithms of integers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a matrix variate slash distribution as a scale mixture of the matrix variate normal and the uniform distributions. We study some properties of the proposed distribution and give maximum likelihood (ML) estimators of its parameters using EM algorithm. We provide an iteratively reweighting algorithm to compute the ML estimates. Also, we give a small simulation study to show performance of the algorithm. [ABSTRACT FROM AUTHOR]

A blind/no-reference (NR) method is proposed in this paper for image quality assessment (IQA) of the images compressed in discrete cosine transform (DCT) domain. When an image is measured by structural similarity (SSIM), two variances, i.e. mean intensity and variance of the image, are used as features. However, the parameters of original copies are actually unavailable in NR applications; hence SSIM is not widely applicable. To extend SSIM in general cases, we apply Gaussian model to fit quantization noise in spatial domain, and directly estimate noise distribution from the compressed version. Benefit from this rearrangement, the revised SSIM does not require original image as the reference. Heavy compression always results in some zero-value DCT coefficients, which need to be compensated for more accurate parameter estimate. By studying the quantization process, a machine-learning based algorithm is proposed to estimate quantization noise taking image content into consideration. Compared with state-of-the-art algorithms, the proposed IQA is more heuristic and efficient. With some experimental results, we verify that the proposed algorithm (provided no reference image) achieves comparable efficacy to some full reference (FR) methods (provided the reference image), such as SSIM. [ABSTRACT FROM AUTHOR]

The first significant digit patterns arising from a mixture of uniform distributions with a random upper bound are revisited. A closed-form formula for its first significant digit distribution (FSD) is obtained. The one-parameter model of Rodriguez is recovered for an extended truncated Pareto mixing distribution. Considering additionally the truncated Erlang, gamma and Burr mixing distributions, and the generalized Benford law, for which another probabilistic derivation is offered, we study the fitting capabilities of the FSD's for various Benford like data sets from scientific research. Based on the results, we propose the general use of a fine structure index for Benford's law in case the data is well fitted by the truncated Erlang member of the uniform random upper bound family of FSD's. [ABSTRACT FROM AUTHOR]

Given a random variable ξ we present three different constructions of a familyof random variables such thatand such that a mixture of the elements of, either satisfies Benford’s law exactly, or it satisfies Benford’s law with any preassigned degree of accuracy. [ABSTRACT FROM PUBLISHER]

Purpose – Complexity is an important element in axiomatic design theory. The current method for calculating complexity for a system following normal distribution is unbounded and approximate. The purpose of this paper is to present a detailed bounded solution for complexity using design and system ranges on a single function requirement. Design/methodology/approach – This paper discusses the complexitymeasure for a system following a uniform distribution. The complexities of two types of systems, a system performing with a uniform distribution and a system performing on target according to a normal distribution are then considered and compared. The research proposes a complexity measure for a system performing within specification limits with a uniform distribution. In addition, a new concept of relative complexity is proposed. Findings – A bounded solution for complexity for a normal distribution based on the existing assumptions was given which includes bias in addition to variance. The bounded solution was then compared to the existing approximate solution from the variance as well as bias standpoint. It was found that bias has an inappropriately reverse relationship with the bounded solution of complexity. Therefore, complexity cannot be used to approximate the system improvement when the improvement is based on a reduction in bias. Originality/value – The current method for calculating complexity for a system following normal distribution is unbounded and approximate. This paper proposed a complexity measure for a system performing within specification limits with a uniform distribution. [ABSTRACT FROM AUTHOR]

Coherent-ambiguity aversion is defined within the (Klibanoff et al., Econometrica 73:1849-1892, ) smooth-ambiguity model (henceforth KMM) as the combination of choice-ambiguity and value-ambiguity aversion. Five ambiguous decision tasks are analyzed theoretically, where an individual faces two-stage lotteries with binomial, uniform, or unknown second-order probabilities. Theoretical predictions are then tested through a 10-task experiment. In (unambiguous) tasks 1-5, risk aversion is elicited through both a portfolio choice method and a BDM mechanism. In (ambiguous) tasks 6-10, choice-ambiguity aversion is elicited through the portfolio choice method, while value-ambiguity aversion comes about through the BDM mechanism. The behavior of over 75 % of classified subjects is in line with the KMM model in all tasks 6-10, independent of their degree of risk aversion. Furthermore, the percentage of coherent-ambiguity-averse subjects is lower in the binomial than in the uniform and in the unknown treatments, with only the latter difference being significant. The most part of coherent-ambiguity-loving subjects show a high risk aversion. [ABSTRACT FROM AUTHOR]

We derive the exact distribution of summation for random samples from uniform distribution and then compare the exact distribution with the approximated normal distribution obtained by the central limit theorem. To check the similarity between two distributions, we consider five existing normality tests based on the difference between the target normal distribution and empirical distribution: Anderson-Darling test, Kolmogorov-Smirnov test, Cramer-von Mises test, Shapiro-Wilk test and Shaprio-Francia test. For the purpose of comparison, those normality tests are applied to the simulated data. It can sometimes be difficult to derive an exact distribution. Thus, we try two different transformations to find out which transform is easier to get the exact distribution in terms of calculation complexity. We compare two transformations and comment on the advantages and disadvantages for each transformation. [ABSTRACT FROM AUTHOR]