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Probability Distribution for Discrete Random Variables

Probability Distribution for Discrete Random Variables

The probability distribution of a discrete random variable is a graph, table, or formula that specifies the probability associated with each possible value that the random variable can assume. Notation: For a discrete random variable x, p(x) will stand for the probability that the observed value of the random variable is a number x, for example

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Instrumental variables estimation with flexible distribution

Instrumental variables estimation with flexible distribution

available from non-Gaussian disturbances in more general settings though pursuing other approaches to estimation and model selection may be an interesting avenue for other research. 3. Distributions Many distributions could be considered in the generalized IV estimation procedure outlined in the previous section. The use of such distributions as the normal or Laplace would not model distributions that are both thick-tailed and asymmetric, both of which are often observed with economic and financial data. The skewed generalized t, the exponential generalized beta of the second kind, and inverse hyperbolic sine distributions involve a small number of distributional parameters and permit modeling a wider range of data characteristics than the normal, Laplace, t, and many other common distributions. These distributions will be defined with basic properties and special cases summarized. We note that there are many other flexible families of
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Signal Coordination Based on Distribution of Platoon Variables

Signal Coordination Based on Distribution of Platoon Variables

9 3. DATA COLLECTION 3.1 Data Collection To study the actual distribution of the speed and headway of platoon vehicles, local data were collected. These data were collected on Texas Avenue, College Station, Texas, as shown in Figure 1. To avoid over-saturated conditions, the data were collected during non-peak hours of weekdays. The actual data collected were vehicle headway and the vehicles’ travel time on a link of a certain length. Four data collection locations were selected to study platoon variables distribution over different link lengths. They were at the upstream, midsection, downstream and further downstream locations of the link, having distances of 620 feet, 1200 feet, 1870 feet and 2370 feet from the upstream intersection. The downstream intersection however, is actually located between the downstream (1870 feet) location and the further downstream (2370 feet) location. Since it can be observed that the signals were coordinated well between these two intersections and that platoons can pass though these two intersection without reducing their speeds, the effect of the downstream intersection can be neglected and the measure time is the actual travel time for 2370 feet link.
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Minimax and Adaptive Estimation of Covariance Operator for Random Variables Observed on a Lattice Graph

Minimax and Adaptive Estimation of Covariance Operator for Random Variables Observed on a Lattice Graph

applications including imaging analysis and fMRI studies, random variables are observed on a lattice graph. In such a setting, it is important to account for the lattice structure when estimating the covariance operator. In this article, we consider both minimax and adaptive estimation of the covariance operator over collections of polynomially decaying and exponentially decaying parameter spaces. We first establish the minimax rates of convergence for estimating the covariance operator under the operator norm. The results show that the dimension of the lattice graph significantly affects the optimal rates convergence, often much more so than the dimension of the random variables. We then consider adaptive estimation of the covariance operator. A fully data-driven block thresholding procedure is proposed and is shown to be adaptively rate optimal
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Children of Senegal River Basin show the highest prevalence of Blastocystissp  ever observed worldwide

Children of Senegal River Basin show the highest prevalence of Blastocystissp ever observed worldwide

It has long been suggested that the pathogenesis of Blastocystis sp. may be dependent upon ST but recent epidemiological data remain contradictory [8,29,33-36]. Nevertheless, the likely pathogenic power of Blastocystis sp. coupled to its high prevalence in the human popula- tion raise crucial questions about its current burden in public health. Consequently, information on the preva- lence of the parasite and the distribution of STs are starting to emerge in still poorly studied geographic areas as Africa. To date the available data concern only few African countries of the North and West such as Egypt [21,37,38], Libya, Nigeria, and Liberia [5] and one Eastern African country, Tanzania [39]. Therefore, the aim of the present study was to reinforce the picture of Blastocystis sp. prevalence and ST distribution in Africa by performing the first survey of this parasite in Senegal.
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Global lightning distribution and whistlers observed at Dunedin, New Zealand

Global lightning distribution and whistlers observed at Dunedin, New Zealand

//ghrc.msfc.nasa.gov). Red dots mark AWD locations in New Zealand and Hungary, and their geomagnetic conjugates. The heavy black lines show the preferred plasmaspheric propagation paths from NLK to Dunedin identified by Clilverd et al. (1992). Entry points are shown by white dots, and exit points by white diamonds. Bearings between 55 ◦ and 75 ◦ are indicated by the black wedge centred on Dunedin. at Wellington, New Zealand, was most likely to propagate along ducts at either the magnetic longitude of the source or the receiver. Shimakura et al. (1987) and Ladwig and Hughes (1989) found that transmission loss was minimised for paths aligned with the source or receiver magnetic merid- ian. These observations suggest that the whistlers originating from lightning strokes on the west coast of Central America either enter a duct close to the source region or near to the conjugate point. Is it possible to discriminate between these two options? There are two principle considerations: the relative attenuation incurred along each of these paths and the applicable conditions for refraction between the Earth- ionosphere waveguide and magnetospheric ducts.
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How many variables are needed to express an existential positive query?

How many variables are needed to express an existential positive query?

and, a query using k variables clearly has width at most k. Within this article, all queries dealt with are relational and first-order. In the setting of query evaluation, the number of variables is a measure of prime and crucial interest. A first reason for this is that the natural bottom-up algorithm for evaluating a first-order query on a finite structure exhibits, in general, an exponential dependence on the number of variables; it also runs in polynomial-time when a constant bound is placed on the number of variables [22]. Furthermore, there are complexity classification theorems [18, 15, 10, 11] on classes of Boolean queries in which the number of variables emerges as the decisive measure for describing whether or not a class of Boolean queries enjoys tractable query evaluation; in particular, these classification theorems show that, if a
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Are Macroeconomic Variables Useful for Forecasting the Distribution of U.S. Inflation?

Are Macroeconomic Variables Useful for Forecasting the Distribution of U.S. Inflation?

Surely such information cannot be delivered by PC-type models that deal only with predicting average inflation. We find strong empirical evidence of predictability of U.S. core monthly inflation, for which we find that indicators of economic activity are useful in forecasting its distribution, especially when using unemployment rate and housing starts. Importantly, the empirical findings apply to a forecast evaluation period that is intentionally chosen to be post 1984, when the existing literature shows that macroeconomic indicators are not relevant to predict future average inflation. To the best of our knowledge this empirical evidence is new in the US inflation forecasting literature. We attribute this result to the ability of our approach to account for the varying predictive effect of economic indicators on core inflation at different quantiles of its distribution. For some indicator variables, we also find an asymmetric effect in the sense that an indicator is more relevant on the lower part of the forecasting distribution than the upper part (and vice versa, depending on the indicator considered). These observed quantile effects take place far away from the center of the distribution, making them difficult to be detected with approaches (like PC-type models) that solely focus on evaluating the relevance of these variables in predicting the conditional mean.
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A Positive Theory of Economic Growth and the Distribution of Income

A Positive Theory of Economic Growth and the Distribution of Income

an economy grows? To answer this question we build a model of a labor economy in which consumers have diverse productivity. The government imposes a linear income tax which funds equal per capita redistribution. The tax rate is set in a sequence of single issue election in which the median productivity individual is decisive. Economic growth is the re- sult of using a learning by doing technology, so higher taxes discourage labor causing the growth rate of the economy to fall. The distribution of productivity can widen due to an exogenous increase in technological specialization. This causes voters to raise the equilibrium tax rate and reduce growth. The distribution of pre-tax income widens. We calibrate the model using data from the U.S., U.K. and France. The results of the calibration show that the model is consistent with the facts about changes in income distribution over time in developed countries.
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Choice of positive distribution law for nuclear data

Choice of positive distribution law for nuclear data

Abstract. Nuclear data evaluation fi les in the ENDF6 format provide mean values and associated uncertainties for physical quantities relevant in nuclear physics. Uncertainties are denoted as D in the format description, and are commonly understood as standard deviations. Uncertainties can be completed by covariance matrices. The evaluations do not provide any indication on the probability density function to be used when sampling. Three constraints must be observed: the mean value, the standard deviation and the positivity of the physical quantity. MENDEL code generally uses positively truncated Gaussian distribution laws for small relative standard deviations and a lognormal law for larger uncertainty levels (>50%). Indeed, the use of truncated Gaussian laws can modify the mean and standard deviation value. In this paper, we will make explicit the error in the mean value and the standard deviation when using different types of distribution laws. We also employ the principle of maximum entropy as a criterion to choose among the truncated Gaussian, the fi tted Gaussian and the lognormal distribution. Remarkably, the difference in terms of entropy between the candidate distribution laws is a function of the relative standard deviation only. The obtained results provide therefore general guidance for the choice among these distributions.
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The Conspicuous Lessons and Positive Impacts Observed Due to COVID-19 in Indian Economy

The Conspicuous Lessons and Positive Impacts Observed Due to COVID-19 in Indian Economy

3 Conclusion To conclude, besides the obvious negative effects, COVID-19 pandemic has certain positive effects too and poses a great learning experience for the world. It is the crisis which has brought forward the multiple good things which can be continued in future as well. The environment, for instance, has been observed to get replenished owing to this crisis. However, after the pandemic is over, if the economic activities revive, the concentration of pollutants and green-house gases are likely to shoot up again. Thus, there is a need for sustainable environment which can be induced with long term structural changes. The positive impacts which have come to forefront like the booming ecommerce, change in lifestyle and consumerism should be continued after the pandemic is over. If the impacts can be so encouraging during a deadly crisis, then a ‘normal’ situation is ought to have a much better economy. The administration should learn from the lessons during the outbreak to understand the vulnerability of the migrants and other marginalised sections and should now include policy measures for them in every -possible economic reform. Also, better distribution and stricter vigilance is needed to ensure that any further catastrophe do not throw them into such hardships again. It is highly important for India now to focus on indigenous development which got a kick start during the pandemic. The science, innovation and research have got a boost to improve during the crisis which needs to be carried on for India to emerge as a self-dependent economy. There is a high chance for such positive effects to float in the economy even after the pandemic is over, but the citizens, administration and policy makers need to realise the vulnerabilities which have surfaced during this crisis and learn from the lessons observed during the outbreak to come up with enhanced measures to have better experience in the coming days in different spheres of the economy.
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The observed distribution of spectroscopic binaries from the Anglo-Australian planet search

The observed distribution of spectroscopic binaries from the Anglo-Australian planet search

The locations of these stars on a HIPPARCOS-based HR diagram, along with a summary of the isochrone fits, are shown in Figs 3(a) and (b), respectively. We also show the distribution of eccentricity versus period in Fig. 4. We find that the companions to HD 121384 and HD 175345 have very high eccentricities for companions with orbital periods below 1000 d, placing them in the extreme upper tail of the distribution in this parameter space. We also find a few of the longer period companions that have not been fully constrained yet due to the limited baseline of the data have moderate to high eccentricity. Although the periods of the orbits could be significantly longer, the eccentricities are rather well constrained with the current
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The impact of the observed baryon distribution in haloes on the total matter power spectrum

The impact of the observed baryon distribution in haloes on the total matter power spectrum

0 Figure 16. Top row The influence of correcting the halo abundance for the halo mass decrease due to baryonic processes. The dark and light gray bands indicate the 1 % and 5 % intervals. The left-hand panel shows model nocb , which effectively assumes that the baryons missing from haloes are redistributed far beyond r 200m,obs on linear scales. The right-hand panel shows model cb , which adds the missing halo baryons in a uniform profile outside but near r 200m,obs . The red, lightly-shaded region for k > 10 h Mpc − 1 indicates the scales where our model is is not a good indicator of the uncertainty because the stellar component is not varied. The lines are colour-coded by γ 0 ≡ γ(m 500c → 0 ) , the extrapolated power-law slope of the hot gas density profiles between r 500c,obs and r 200m,obs , with lower values of γ 0 corresponding to flatter slopes. We show the power spectrum response with (our fiducial models, solid lines) and without (dashed lines) the correction for the halo masses applied. In the latter case, we find more power than in the DMO case at large scales because the abundance of low-mass haloes is overestimated due to not accounting for their mass loss compared to their DMO equivalents. Bottom row The ratio of the power spectrum with and without correction for the halo masses. Models with flatter slopes, i.e. lower values of γ 0 , reach the cosmic baryon fraction at r 200m,obs for lower halo masses, resulting in the same total mass-abundance relation as the DMO equivalent halo for a larger range of halo masses and thus more similar power spectra.
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Modeling Sequences of Long Memory Positive Weakly Stationary Random Variables

Modeling Sequences of Long Memory Positive Weakly Stationary Random Variables

Models introduced in this paper have several potential applications in empirical studies in a variety of fields. From the perspective of the dynamic heteroscedasticity, our models offer a framework that naturally extends short-memory GARCH models, including finite and infinite second moment. In the former case, the autocovariances are non-summable, which satisfies the long-memory criterion of McLeod and Hipel (1978). In the paper we also show a method to obtain the compound model which nests both the basic long-memory and GARCH models. This gives researchers a tool to distinguish between the cases of summable and non-summable autocovariances in the volatility process of real-world financial data.
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HLA Cw6 positive patients with psoriasis show improved response to methotrexate treatment

HLA Cw6 positive patients with psoriasis show improved response to methotrexate treatment

METHODS: ............................................................................................................................................................... 2 EXTENDED RESULTS ........................................................................................................................................... 4 SUPPLEMENTARY TABLES ................................................................................................................................ 5 T ABLE S1. T HE OBSERVED AND EXPECTED FREQUENCY OF GENOTYPES IN THE COMBINED PATIENT COHORTS 1 . 5 T ABLE S2. C UMULATIVE LONG - TERM INCIDENCE TREATMENT LIMITING AE SPECTRUM IN MTX TREATMENT FOR PARENT AND HLA STATUS COHORT 1 ........................................................................................................................... 6 T ABLE S3. C UMULATIVE LONG - TERM INCIDENCE TREATMENT LIMITING AE SPECTRUM IN MTX TREATMENT FOR BOTH PATIENT COHORTS 1 .............................................................................................................................................. 7 T ABLE S4. C UMULATIVE LONG - TERM INCIDENCE AE SPECTRUM IN MTX TREATMENT FOR BOTH PATIENT COHORTS 1 ................................................................................................................................................................................. 8 SUPPORTING FIGURES ........................................................................................................................................ 9 F IGURE S1. C ONSUMPTION OF TOPICAL PSORIASIS TREATMENTS IN PATIENTS ACHIEVING 1- YEAR OF
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Epstein-Barr Virus-Positive Cancers Show Altered B-Cell Clonality

Epstein-Barr Virus-Positive Cancers Show Altered B-Cell Clonality

Epstein-Barr virus (EBV) is a human herpesvirus, and like the other seven human herpesviruses, EBV establishes lifelong persistence in the human host, a state that is termed latency. Over 90% of adults are infected with EBV by age 50, and at any given time, a third of seropositive persons shed infectious virus in saliva (8). Once infected, the EBV genome is continuously present in circulating CD38-positive memory B cells (9). During this state, no or only a very few viral mRNAs are transcribed. Spontaneous mononucleosis or immunodeficiency-associated reactivation events result in amplifi- cation of EBV-infected cells and extended mRNA transcription. De novo B-cell and epithelial cell infection are associated with widespread, promiscuous transcription across the entire ⬃ 172,000-bp viral genome. Unlike the other human herpesviruses, except for human herpesvirus 8 (Kaposi sarcoma-associated herpesvirus), EBV is strongly associated with cancer and able to transform primary human B cells in culture. There exists sufficient evidence to associate EBV infection with Burkitt lymphoma (BL), Hodgkin’s disease (HD), posttransplant lymphoproliferative disease (PTLD), and rare forms of non-Hodgkin’s lymphoma, such as those localized to the central nervous system in AIDS patients (AIDS-CNS lymphoma) (1). These cancers originate from B cells, and the virus is present at multiple copies in every tumor cell. The exception is HD, where only a fraction of the proliferative compartment, the Reed-Sternberg cell, is EBV positive. HD is one example of a cancer that is convincingly and causally virus associated, yet the virus is present in only a fraction of the cells in the lesion. In addition, EBV is associated with the epithelial cancers nasopharyngeal carcinoma (NPC) and gastric cancer. Here again, the EBV genome and EBV mRNAs are found in every single tumor cell. Because cancers are a heterogeneous group of diseases, the EBV association ranges from ⬎ 90% in AIDS-CNS lymphoma to approximately 10% in gastric cancer (10). Furthermore, many associations depend on geographic locale. For instance, most cases of EBV-positive NPC are observed in southern China and among the Inuit in the Arctic (11).
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Are Macroeconomic Variables Useful for Forecasting the Distribution of U S  Inflation?

Are Macroeconomic Variables Useful for Forecasting the Distribution of U S Inflation?

individual leading indicators can be combined to deliver better forecast accuracy. A great number of studies on average inflation forecasting report that combining forecasts tends to outperform individual forecasts. We provide new empirical evidence of predictability of US core monthly inflation (core inflation is measured after excluding food and energy), for which we find that indicators of economic activity are useful in forecasting its distribution, especially when using unem- ployment rate, housing starts, and the term spread. Interestingly, the empirical findings apply to a forecast evaluation period that is intentionally chosen to be post 1984, when the existing literature shows that macroeconomic indicators are not relevant to predict future average inflation. We attribute this result to the ability of the semi-parametric method to account for the differing relationship between inflation and indicators at different quantiles of inflation. For some indicator variables, we also find an asymmetric effect in the sense that an indicator is more relevant on the lower part of the forecasting distribution than the upper part (and viceversa, depending on the indicator considered). These observed quan- tile effects take place far away from the center of the distribution, making them difficult to be detected with approaches (like PC-type models) that solely focus on evaluating the relevance of these variables in predicting the conditional mean. To illustrate the aforemen- tioned effects, we consider the late 1990s when inflation was at historically low levels despite the possible rising inflation signaled by most indicators of economic activity. During this period, unemployment rate was decreasing, and went even below 4% at the beginning of 2000. Our analysis shows that when unemployment rate is incorporated into forecasting the future inflation distribution, the “expected” negative relationship between unemployment and inflation was mostly at work in the tails of the inflation distribution, and more so at lower quantiles. This observation is of practical relevance to policy makers when assessing the possibility of such events as deflation, which was the case at the beginning of 1998.
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A new generalized Weibull distribution generated by gamma random variables

A new generalized Weibull distribution generated by gamma random variables

Now, we shall apply formal goodness-of-fit tests in order to verify which distribution fits better these real data sets. We consider the Crame´r–von Mises ðW  Þ and Anderson–Darling ðA  Þ statistics, which are described in details by [35] . In gen- eral, the smaller the values of these statistics, the better the fit to the data. The statistics W  and A  for all the models are listed in Table 4 . Note that the new C-EW distribution out- performs all their sub-models as well as the four-parameter C2- EW, BW and KwW distributions. Notice that the C-EW distri- bution is clearly a competitive model for the C2-EW, BW and KwW distributions, since they have the same number of parameters. Therefore, the new model may be an interesting alternative to the other models available in the literature for modeling positive real data.
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The Influence of Press Variables and the Measurement of Show Through of Paper

The Influence of Press Variables and the Measurement of Show Through of Paper

The TAPPI Opacity of Batch B Ink Film Thicknesses and Their Reverse Sides on 70 lb Uncoated Smooth Finish Offset Paper with Various Levels of Speed and a.. 25% Pigment Concentration 202.[r]

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The Equilibrium Distribution of Counting Random Variables

The Equilibrium Distribution of Counting Random Variables

Received July 1, 2011; revised August 3, 2011; accepted August 15, 2011 Abstract We study the high order equilibrium distributions of a counting random variable. Properties such as moments, the probability generating function, the stop—loss transform and the mean residual lifetime, are derived. Ex- pressions are obtained for higher order equilibrium distribution functions under mixtures and convolutions of a counting distribution. Recursive formulas for higher order equilibrium distribution functions of the

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