scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (3) ◽  
pp. 714-716 ◽  
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

scholarly journals On a family of prior distributions for a class of Bayesian search models

1993 ◽  
Vol 25 (03) ◽  
pp. 714-716
Author(s):  
K. D. Glazebrook
Keyword(s):  
Conjugate Prior ◽  
Prior Distributions ◽  
Search Models ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
The One ◽  
Two Parameters ◽  
Two Parameter ◽  
Conjugate Prior Distributions

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.

scholarly journals The modified beta transmuted family of distributions with applications using the exponential distribution

PLoS ONE ◽  
2021 ◽  
Vol 16 (11) ◽  
pp. e0258512
Author(s):  
Phillip Oluwatobi Awodutire ◽  
Oluwafemi Samson Balogun ◽  
Akintayo Kehinde Olapade ◽  
Ethelbert Chinaka Nduka
Keyword(s):  
Exponential Distribution ◽  
Real Life ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Life Time ◽  
Time Data ◽  
New Family ◽  
Special Cases ◽  
The Family ◽  
Family Of Distributions

In this work, a new family of distributions, which extends the Beta transmuted family, was obtained, called the Modified Beta Transmuted Family of distribution. This derived family has the Beta Family of Distribution and the Transmuted family of distribution as subfamilies. The Modified beta transmuted frechet, modified beta transmuted exponential, modified beta transmuted gompertz and modified beta transmuted lindley were obtained as special cases. The analytical expressions were studied for some statistical properties of the derived family of distribution which includes the moments, moments generating function and order statistics. The estimates of the parameters of the family were obtained using the maximum likelihood estimation method. Using the exponential distribution as a baseline for the family distribution, the resulting distribution (modified beta transmuted exponential distribution) was studied and its properties. The modified beta transmuted exponential distribution was applied to a real life time data to assess its flexibility in which the results shows a better fit when compared to some competitive models.

scholarly journals A Flexible Approach to Modeling Over-, Under- and Equidispersed Count Data in IRT: The Two-Parameter Conway-Maxwell-Poisson Model

2021 ◽  
Author(s):  
Marie Beisemann
Keyword(s):  
Count Data ◽  
Divergent Thinking ◽  
Poisson Model ◽  
Likelihood Method ◽  
Marginal Maximum Likelihood ◽  
Irt Model ◽  
Special Cases ◽  
The One ◽  
Two Parameter ◽  
Poisson Counts

Several psychometric tests generate count data, e.g. the number of ideas in divergent thinkingtasks. The most prominent count data IRT model, the Rasch Poisson Counts Model (RPCM)assumes constant discriminations across items as well as the equidispersion assumption of thePoisson distribution (i.e., E(X) = Var(X)), considerably limiting modeling flexibility. Violationsof these assumptions are associated with impaired ability, reliability, and standard error estimates.Models have been proposed to loose the one or the other assumption. The Two-Parameter PoissonCounts Model (2PPCM) allows varying discriminations but retains the equidispersion assumption.The Conway-Maxwell-Poisson Counts Model (CMPCM) that allows for modeling equi- but alsoover- and underdispersion (more or less variance than implied by the mean under the Poisson distribution)but assumes constant discriminations. The present work introduces the Two-ParameterConway-Maxwell-Poisson (2PCMP) model which generalizes the RPCM, the 2PPCM, and the CMPCM(all contained as special cases) to allow for varying discriminations and dispersions withinone model. A marginal maximum likelihood method based on a fixed quadrature Expectation-Maximization (EM) algorithm is derived. Standard errors as well as two methods for latent abilityestimation are provided. An implementation of the 2PCMP model in R and C++ is provided. Twosimulation studies examine the model’s statistical properties and compare the 2PCMP model toestablished methods. Data from divergent thinking tasks are re-analyzed with the 2PCMP modelto illustrate the model’s flexibility and ability to test assumptions of special cases.

scholarly journals Simulation of Spatial Spread of the COVID-19 Pandemic on the Basis of the Kinetic-Advection Model

Physics ◽  
2021 ◽  
Vol 3 (1) ◽  
pp. 85-102
Author(s):  
Vladimir V. Aristov ◽  
Andrey V. Stroganov ◽  
Andrey D. Yastrebov
Keyword(s):  
Geographical Location ◽  
Spreading Rate ◽  
Equation Model ◽  
Dynamic Density ◽  
Spatial Spread ◽  
One Dimensional ◽  
Average Spreading ◽  
The One ◽  
Two Parameters ◽  
Two Parameter

A new two-parameter kinetic equation model is proposed to describe the spatial spread of the virus in the current pandemic COVID-19. The migration of infection carriers from certain foci inherent in some countries is considered. The one-dimensional model is applied to three countries: Russia, Italy, and Chile. Both their geographical location and their particular shape stretching in the direction from the centers of infection (Moscow, Lombardy, and Santiago, respectively) make it possible to use such an approximation. The dynamic density of the infected is studied. Two parameters of the model are derived from known data. The first is the value of the average spreading rate associated with the transfer of infected persons in transport vehicles. The second is the frequency of the decrease in numbers of the infected as they move around the country, associated with the arrival of passengers at their destination. An analytical solution is obtained. Simple numerical methods are also used to perform a series of calculations. Calculations us to make some predictions, for example, about the time of recovery in Russia, if the beginning of recovery in Moscow is known.

scholarly journals Most Probably Intersecting Families of Subsets

2012 ◽  
Vol 21 (1-2) ◽  
pp. 219-227 ◽  
Author(s):  
GYULA O. H. KATONA ◽  
GYULA Y. KATONA ◽  
ZSOLT KATONA
Keyword(s):  
Exact Solution ◽  
Maximum Size ◽  
Proper Subset ◽  
Analogous Problem ◽  
New Family ◽  
Intersecting Family ◽  
The Family ◽  
Intersecting Families ◽  
The One ◽  
Element Set

Let be a family of subsets of an n-element set. It is called intersecting if every pair of its members has a non-disjoint intersection. It is well known that an intersecting family satisfies the inequality || ≤ 2n−1. Suppose that ||=2n−1 + i. Choose the members of independently with probability p (delete them with probability 1 − p). The new family is intersecting with a certain probability. We try to maximize this probability by choosing appropriately. The exact maximum is determined in this paper for some small i. The analogous problem is considered for families consisting of k-element subsets, but the exact solution is obtained only when the size of the family exceeds the maximum size of the intersecting family only by one. A family is said to be inclusion-free if no member is a proper subset of another one. It is well known that the largest inclusion-free family is the one consisting of all $\lfloor \frac{n}{ 2}\rfloor$-element subsets. We determine the most probably inclusion-free family too, when the number of members is $\binom{n}{ \lfloor \frac{n}{ 2}\rfloor} +1$.

scholarly journals Joint spectral radius and ternary hermite subdivision

2021 ◽  
Vol 47 (2) ◽  
Author(s):  
M. Charina ◽  
C. Conti ◽  
T. Mejstrik ◽  
J.-L. Merrien
Keyword(s):  
Spectral Radius ◽  
Joint Spectral Radius ◽  
Subdivision Schemes ◽  
New Family ◽  
Polygonal Region ◽  
The Family ◽  
Higher Regularity ◽  
Two Parameter ◽  
Insight Into ◽  
Hermite Subdivision

AbstractIn this paper we construct a family of ternary interpolatory Hermite subdivision schemes of order 1 with small support and ${\mathscr{H}}\mathcal {C}^{2}$ H C 2 -smoothness. Indeed, leaving the binary domain, it is possible to derive interpolatory Hermite subdivision schemes with higher regularity than the existing binary examples. The family of schemes we construct is a two-parameter family whose ${\mathscr{H}}\mathcal {C}^{2}$ H C 2 -smoothness is guaranteed whenever the parameters are chosen from a certain polygonal region. The construction of this new family is inspired by the geometric insight into the ternary interpolatory scalar three-point subdivision scheme by Hassan and Dodgson. The smoothness of our new family of Hermite schemes is proven by means of joint spectral radius techniques.

On Three New Proteocephalids (Cestoda) and a Revision of the Genera of the Family

Parasitology ◽  
1925 ◽  
Vol 17 (4) ◽  
pp. 370-394 ◽  
Author(s):  
W. N. F. Woodland
Keyword(s):  
General Scheme ◽  
Cortical Region ◽  
Present Communication ◽  
New Family ◽  
The Family ◽  
Original Family ◽  
The Subject ◽  
The One

When La Rue (1914 a) published his exhaustive monograph on the Proteocephalidae, all the then-known species of this family were, with one exception, shown to be very much alike. To substantiate this statement it will suffice to mention that all the six genera, into which La Rue grouped the species, were chiefly based upon trivial characters of the scolex and the distribution of the testes. The one exception referred to was the species which he re-named Monticellia coryphicephala (Monticelli), and this species differed from all the others in the remarkable and relatively deep-seated character of its principal genital organs being situated in the cortical region of the parenchyma instead of in the medullary. This one exception was promptly transferred by La Rue to a distinct new family, the Monticellidae, and the consequence was that he was still left dependent upon the aforesaid trivial characters as bases for his genera in the original family. Since 1914 however we have come to know of some other Proteocephalids exhibiting similar deep-seated differences of structure, and we are therefore in a position to re-consider the classification of the Proteocephalidae on broader lines, including Monticellia coryphicephala in that family. The general scheme of this re-classification I have already outlined in a paper (Woodland, 1925 a) which will be published either before or shortly after the present communication, and it is my purpose, in this latter, to justify the suggestions there referred to by discussing the subject in some detail. Before attempting this, however, I shall describe the structure of three new Proteocephalids, two from India (in a frog and a Varanid lizard) and one from the Sudan (in a Siluroid fish).

Sign in / Sign up

Export Citation Format

Share Document