Kinds Of Distributions Research Articles

Portfolio selection based on upper and lower exponential possibility distributions

In this paper, two kinds of possibility distributions, namely, upper and lower possibility distributions are identified to reflect experts' knowledge in portfolio selection problems. Portfolio selection models based on these two kinds of distributions are formulated by quadratic programming problems. It can be said that a portfolio return based on the lower possibility distribution has smaller possibility spread than the one on the upper possibility distribution. In addition, a possibility risk can be defined as an interval given by the spreads of the portfolio returns from the upper and the lower possibility distributions to reflect the uncertainty in real investment problems. A numerical example of a portfolio selection problem is given to illustrate our proposed approaches.

Changes in Web client access patterns: Characteristics and caching implications

Understanding the nature of the workloads and system demands created by users of the World Wide Web is crucial to properly designing and provisioning Web services. Previous measurements of Web client workloads have been shown to exhibit a number of characteristic featuress however, it is not clear how those features may be changing with time. In this study we compare two measurements of Web client workloads separated in time by three years, both captured from the same computing facility at Boston University. The older dataset, obtained in 1995, is well known in the research literature and has been the basis for a wide variety of studies. The newer dataset was captured in 1998 and is comparable in size to the older dataset. The new dataset has the drawback that the collection of users measured may no longer be representative of general Web userss however, using it has the advantage that many comparisons can be drawn more clearly than would be possible using a new, different source of measurement. Our results fall into two categories. First we compare the statistical and distributional properties of Web requests across the two datasets. This serves to reinforce and deepen our understanding of the characteristic statistical properties of Web client requests. We find that the kinds of distributions that best describe document sizes have not changed between 1995 and 1998, although specific values of the distributional parameters are different. Second, we explore the question of how the observed differences in the properties of Web client requests, particularly the popularity and temporal locality properties, affect the potential for Web file caching in the network. We find that for the computing facility represented by our traces between 1995 and 1998, (1) the benefits of using size-based caching policies have diminisheds and (2) the potential for caching requested files in the network has declined.

Comparison of Road Network Patterns with Respect to Travel Distance and Passing Volume

In order to reveal some characteristics of urban physical structures, regarding to space utilization especially to movement, we introduce two kinds of distributions which are distance distribution and distribution of passing volume in a given apace (road network). Using these distributions we make a comparison between a radial network and a grid network under the condition that the total length of a road network is constant.

The distribution δ( k) ( P ± i0 − m2)

In this note we give a sense to certain kinds of distribution δ ( k) ( P ± i0 − m 2) using essentially the causal version of the distribution Bochner (cf. Trione, 1976). As a consequence we obtain the convolution products of distributions δ ( k) ( P ± i0).

Characteristics of whistler wave normal distributions at the exit of low‐latitude duct

AbstractAccording to the direction‐finding observation of whistler at low latitudes, the whistlers come from a narrow region of the zenith and exhibit morphology at ionospheric exits. When ionospheric transmission characteristics of the very low‐frequency (VLF) radio wave emitted to the ground from the magnetic field‐aligned duct due to the irregularity of the ionosphere are computed, or when the results of the VLF direction‐finding observation on the ground are discussed, distribution of the wave normal of the radio wave at the duct exits is important.Here, the wave‐normal distribution of the VLF whistlers at the duct exit, namely the wave normal of the VLF whistlers at each part of the duct exit, is computed by means of the two‐dimensional ray tracing based on the duct propagation model assuming low latitudes. It was found that there are two kinds of wave‐normal distributions, i.e., upward and downward. The cause of the generation of the two kinds of distributions was clarified qualitatively by the duct‐propagation theory. Also, the factors for various characteristics of the wave‐normal distributions at the duct exit were investigated. Especially, for the downward wave‐normal distributions, there is a region at the center of the duct where the wave normals are directed vertically downward due to the effect of the vertical gradient of the ionosphere applied in the duct. This region contributes to the transmission of the whistler to the ground.

Distributions slanted to the right

We solve Problem 234 in Statistica Neerlandica by introducing the concept of slantedness. Distributions with a decreasing Lebesgue density are slanted to the right. This is no longer true for distributions on a lattice with decreasing density. Both kinds of distributions have positive central odd moments.

Dependability modeling using Petri-nets

This paper describes a methodology to construct dependability models using generalized stochastic Petri nets (GSPN) and stochastic reward nets (SRN). Algorithms are provided to convert a fault tree (a commonly used combinatorial model type) model into equivalent GSPN and SRN models. In a fault-tree model, various kinds of distributions can be assigned to components such as defective failure-time distribution, nondefective failure-time distribution, or a failure probability. The paper describes subnet constructions for each of these different cases, and shows how to incorporate repair in these models. >

Mössbauer study of amorphous Fe2RE (RE=Ce, Er) alloys

Among amorphous Fe2RE (RE=Er, Ce, Gd, La, Pr, Sm, Dy, Ho) alloys, Fe2Ce exhibits a tendency toward short range order, while the other Fe2RE compounds show clustering. However, we have almost no information about environments around Fe atoms. Using Mossbauer spectroscopy we have determined the quadrupole splitting distributionsP(QS) of two representative amorphous Fe2RE (RE=Ce, Er) alloys, leading to local environments of Fe atoms. The analysis of the mixed magnetic dipole and quadrupole interactions in Fe2Er shows two kinds of electrical field gradients (EFT) with the positive and negative signs in the sample, indicating a random packing of Fe atoms. Furthermore, the analyzed quadrupole splitting distributionP(QS) of Fe2Er also supports random packing in this amorphous alloy. On the other hand, the amorphous Fe2Ce alloy shows two kinds of distributions of quadrupole splitting; the major component indicating random packing and the minor component Ce-rich Ce-Fe clusters.

Flow of a viscoplastic fluid on a rotating disk

The equations describing the flow of a viscoplastic fluid on a rotating disk are derived and are solved by perturbation technique and numerical computation respectively for 2 cases. This makes it possible to calculate the thickness distribution of film. Two kinds of distribution of thickness have been found. For the viscoplastic fluid for which both viscosity and yield stress are independent of radial coordinate r, the thickness h decreases with increasing r. For a Bingham fluid for which both viscosity and yield stress are function of time and r, the thickness h increases with increasing r.

Relationship between surface chlorophyll and chlorophyll in the euphotic zone of the Gulf of California: possible application to estimate primary production with data obtained by remote sensors

The vertical distribution of pigments (chlorophyll a) in the study area showed maximum surface chlorophyll to the north of line 240, subsurface and deep chlorophyll maxima to the South of line 320 and both kinds of distribution between lines 240 and 320. Surface chlorophyll was positively correlated with integrated chlorophyll within the euphotic zone (r = 0.61, p < 0.001). We found a higher linear correlation between the chlorophyll concentration presumably measured by remote sensing and the integrated chlorophyll (r = 0.79, p < 0.001). The estimation of integrated chlorophyll in the euphotic zone from surface chlorophyll was complicated because of the variability of the vertical profiles of pigments for this season. Therefore, we propose a mean normalized profile of pigments for the use of primary production models based on light and phytoplankton biomass. From the mean normalized chlorophyll profile, during winter the Gulf of California can be classified as a mesotrophic region, with a not very prominent subsurface chlorophyll maximun.

General simulated annealing

Simulated annealing is a new kind of random search methods developed in recent years. It can also be considered as an extension to the classical hill-climbing method in AI—probabilistic hill climbing. One of its most important features is its global convergence. The convergence of simulated annealing algorithm is determined by state generating probability, state accepting probability, and temperature decreasing rate. This paper gives a generalized simulated annealing algorithm with dynamic generating and accepting probabilities. The paper also shows that the generating and accepting probabilities can adopt many different kinds of distributions while the global convergence is guaranteed.

The matrix angular central Gaussian distribution

The Riemann space whose elements are m × k ( m ≥ k) matrices X such that X′ X = I k is called the Stiefel manifold and denoted by V k, m . Some distributions on V k, m , e.g., the matrix Langevin (or von Mises-Fisher) and Bingham distributions and the uniform distribution, have been defined and discussed in the literature. In this paper, we present methods to construct new kinds of distributions on V k, m and discuss some properties of these distributions. We investigate distributions of the “orientation” H Z = Z(Z′Z) −1 2 ( ϵV k, m ) of an m × k random matrix Z. The general integral form of the density of H Z reduces to a simple mathematical form, when Z has the matrix-variate central normal distribution with parameter Σ, an m × m positive definite matrix. We may call this distribution the matrix angular central Gaussian distribution with parameter Σ, denoted by the MACG (Σ) distribution. The MACG distribution reduces to the angular central Gaussian distribution on the hypersphere for k = 1, which has been already known. Then, we are concerned with distributions of the orientation H Y of a linear transformation Y = BZ of Z, where B is an m × m matrix such that ∥ B∥ ≠ 0. Utilizing properties of these distributions, we propose a general family of distributions of Z such that H Z has the MACG (Σ) distribution.

Effects of Ag-doping on critical current densities in high T c superconducting materials of YBa 2Cu 3O 7−x

To enhance the critical current density of YBCO superconductors the attempt to add Ag, Ag 2O, AgNO 3 into the materials has been made. No obvious difference on microstructures, such as grain size, orientations, twins, boundaries, microcracks, were observed between pure and doped YBCO specimens. ALCHEMI was used to locate the impurity atoms inside YBCO unit cells. Most of Ag in YBCO Ag-system doped specimens to be found filling in the sinter pores contributes to strengthening the materials and purifying the YBCO matrices. Some Ag + cations entering YBCO lattices and occupying the Cu 2+ or Cu 3+ sites were detected by ALCHEMI. The Ag + substitution for Cu 2+ or Cu 3+ will deteriorate the superconductivity due to the decrease of oxygen absorption abilities of YBCO crystals. The total effect of Ag-doping depends on the competition of the Ag dopants with two kinds of distributions.

The Editor's Corner: The Exponential Distribution

Random number generators are built into most home computers now, so many more people are getting a chance to use them then ever before. Usually, a 'random number generator' manufactures, on demand, numbers t between 0 and 1, produced in such a manner as to be equally likely to reside anywhere in that interval. More precisely, if [a, b] is a subinterval of (0,1), then the probability that the next random number ( lies in [a, b] is b a. For an ideal random number generator that statement would be true for every [a, b] c (0,1). Given such a supply of random numbers, it is easy to produce other kinds of distributions by various manipulations. To choose a number X uniformly at random in the interval (7,13), for instance, we would write X = 7 + 6t, where ( is a random number. Again, to choose an integer L uniformly at random between 0 and n, just set L = [ (n + 1)J, in which ( is a random number and '1 ',is the greatest integer function. Sometimes we want numbers that aren't equally likely to turn up everywhere, but instead are more likely to lie in some places than in others. These can be obtained by twisting random numbers out of shape, and some fearsomely ingenious constructions have been suggested, over the years, in order to achieve various kinds of twists. See Chapter 3 of [3] for accounts of some of these. Among nonuniform distributions one of the most important is the exponential distribution, which describes positive real numbers X that are chosen in such a way that for every t > 0, the probability that X < t is 1 e. It is therefore more likely that X lies between l and 2 (the chance is e-l e-2 = .232), say, than between 8 and 9 (probability e-8 e-9 = .00021), etc. The exponential distribution occurs naturally in many situations. Two categories of these are waiting time problems and particle diffusion problems. In waiting line ('queueing') simulations it is frequently the case that it is more likely that we wait a shorter time and less likely a longer time. Hence in a computer simulation it is often desirable to select the delay times from the exponential distribution. Likewise, when a particle bounces around in a diffusing medium, it is more probable that it will travel a shorter distance D between successive collisions with molecules of the medium than a longer distance. Under reasonable assumptions it isn't hard to show that D obeys the exponential distribution. A question of mathematical interest and beauty, as well as of practical application (a happy combination) is then the following: given a random number generator, how shall we select numbers X that have the exponential distribution? Here's the quick answer (then we'll look at two other ways). First choose a random number (, then calculate X = log (. That's all. We claim that the numbers X that are so produced have the exponential distribution. To see that we need perform only the following calculation ('Prob' means 'the probability of'):

Dry spells in the Alpine country Austria

This paper gives a short survey of the most important results of investigations from a comprehensive book written by the author in German (Nobilis, 1985). Different kinds of distributions were tested to fit the sequences of dry days and to explain the persistence. The considerations are supplemented by Markov chain models up to order four. The graphical presentation of conditional probabilities for the territory of Austria (83,849 km 2) provides valuable aid for understanding the phenomenon of “dry spell” in an Alpine country. The analysis of the average number of sequences of dry days for the main river basins applying harmonic analysis and the presentation of nor-malized harmonic dials show the hydroclimatological differences between various river basins. The statistical considerations of the extreme dry spells for the entire year and for the vegetation period (April–October) give useful hints for a more objective estimation of extreme dry spells in the past. Finally, spectral analysis is used to investigate possible periodicities of extreme dry spells. In this connection, the question of relevant trends is discussed too.

Electroweak corrections to muon pair production in electron-positron annihilation at high energy

The lowest-order radiative corrections to the reaction e + + e − → μ + + μ − are analyzed in the standard SU(2) × U(1) electroweak theory. The virtual corrections are calculated in the on-shell renormalization scheme. The masses of the recently discovered Z-boson and W-boson are used to fix the weak coupling constants. The decay width of the Z-boson is also taken into account. By including the cross section of hard photon emission, various kinds of distribution are obtained both analytically and numerically. The magnitude of the effective axial vector coupling is confirmed to be quite different from that previously taken in the calculations within QED. This difference, which is due to the genuine electroweak corrections, reaches about 10% in angular distribution at the energy around the Z-boson mass, even if the reasonable effect of a hard photon is included.

Age distribution and fertility of populations of the arctic‐alpine species Oxyria digyna

Age distributions and fruit production of populations of Oxyria digyna (L) Hill were studied in Norway and Greenland. The observed age distributions were described by the negative exponential function and by the power function. Three kinds of distributions were observed: steep, flat and bell‐shaped with the corresponding hint production: 33–917, 8–108 and 76–303 fruits per individual. The population with the steep age distributions and high fruit productions were assumed to be increasing. They were found in sites with almost no vegetation (≤10% cover). The populations with the flat age distributions and the low fruit production were assumed to be stable. They were found in sites with a vegetational cover of 50–75%. The populations with the bell‐shaped age distributions and the intermediate fruit productions were assumed to be decreasing. They were found in sites with a closed vegetation (cover ≥100%).

General relationships between wave amplification and particle diffusion in a magnetoplasma

The general conditions for wave generation (γ &gt; 0) or wave absorption (γ &lt; 0) by a given distribution of energetic particles are discussed in the case of electromagnetic waves propagating along the dc magnetic field. It is shown that the nature of the interaction (γ &gt; 0 or γ &lt; 0) can be easily determined by considering the relative position of three curves in the υ∥, υ⊥ plane (where υ∥ and υ⊥ are the parallel and perpendicular velocity of the particle): the isodensity curve, the constant energy curve, and the diffusion curve. For ‘regular’ distribution functions (i.e., distributions which are concave around the origin and for which there are less particles of high energy than particles of low energy) a necessary and sufficient condition for positive growth rate is that the third curve be situated within the area delineated by the other two curves. This geometrical formalism is extended to other kinds of distributions (field‐aligned beams or ring distributions). It is also applied to wave‐particle interactions in multicomponent plasmas. The conclusions which we arrive at are in agreement with previous findings. The analytical demonstration of this geometrical property is given. It is linked with the fact that the equations which govern the wave amplification and the particle diffusion involve the same operator, which is the derivative of the distribution function taken along the diffusion curve. The origin of this property lies in the special form of the Boltzmann‐Vlasov equation.

Use of the LRU stack depth distribution for simulation of paging behavior

Two families of probability distributions were needed for use by a virtual memory simulation model: headway between page fault distributions, and working set size distributions. All members of both families can be derived from the LRU stack depth distribution. Simple expressions for the computation of both kinds of distributions are given. Finally, examples are given of both families of distributions as computed from a published stack depth distribution.

On the Fourier Transform of Causal Distributions

We extend the distributional Bochner formula [1, p. 72, Theorem 26] to certain kinds of distributions. Theorem I.1 gives a formula [Eq. (I.1.14)] which makes it possible to obtain easily the Fourier transform of distributions of the form urn:x-wiley:00222526:media:sapm1976554315:sapm1976554315-math-0001 As applications of the formula (I.1.14) we evaluate the Fourier transforms of the distributions Gα(P±i0, m, n) [Eq. (I.4.1)] and Hα(P±i0,n) [Eq. (II.1.1)]. It follows from Theorem II.3 that Hzk(P±i0,n) is, for 2K≠n+2r, r=0,1..., an elementary solution of the n‐dimensional ultrahyperbolic operator iterated k times.