scholarly journals On Bimodal Offset Cauchy Distribution

2013 ◽  
Vol 9 (1) ◽  
pp. 61-67 ◽  
Author(s):  
S.V.S. Girija ◽  
A.J.V. Radhika ◽  
A.V.Dattatreya Rao
Keyword(s):  
Clinical Trials ◽  
Queuing Theory ◽  
Cauchy Distribution ◽  
Circular Data ◽  
Circular Model ◽  
Circular Distributions ◽  
Directional Component ◽  
Decreasing Failure Rate ◽  
Cauchy Model ◽  
Labour Turnover

Abstract The bivariate Cauchy distribution has received applications in many areas, including biological analyses, clinical trials, stochastic modeling of decreasing failure rate life components, study of labour turnover, queuing theory and reliability (Nayak (1987) and Lee and Gross (1991)). In the study of biological analyses, clinical trials and reliability circular distributions will yield suitable results. Circular data arises in a number of different areas such as geological, meteorological, biological and industrial sciences. It is not suggestive to use standard statistical techniques to model circular data, due to the circular geometry of the sample space (p.2 Jammalamadaka and Sen Gupta (2001). It is possible to construct a circular model by transforming a bivariate linear random variate to just its directional component and the resultant model is called ‘offset distribution’. In the literature most of the available circular models were constructed by wrapping a linear model. In recent years some wrapped models were constructed by Dattatreya Rao et al (2007). Here an attempt is made to exploit method of offsetting on Bivariate Cauchy distribution to construct a circular model named by us “OFFSET CAUCHY DISTRIBUTION (OC)”. The characteristic function of the Offset Cauchy model is derived and its characteristics are discussed.

scholarly journals Characterizations of the Cauchy distribution associated with integral transforms

2020 ◽  
Vol 57 (3) ◽  
pp. 385-396
Author(s):  
Kazuki Okamura
Keyword(s):  
Cauchy Distribution ◽  
Integral Transforms ◽  
Mellin Transforms ◽  
Cauchy Model

AbstractWe give two new simple characterizations of the Cauchy distribution by using the Möbius and Mellin transforms. They also yield characterizations of the circular Cauchy distribution and the mixture Cauchy model.

scholarly journals Generalized Cardioid Distributions for Circular Data Analysis

Stats ◽  
2021 ◽  
Vol 4 (3) ◽  
pp. 634-649
Author(s):  
Fernanda V. Paula ◽  
Abraão D. C. Nascimento ◽  
Getúlio J. A. Amaral ◽  
Gauss M. Cordeiro
Keyword(s):  
Data Analysis ◽  
Structural Properties ◽  
Real Data ◽  
Linear Representation ◽  
Circular Data ◽  
Mathematical Properties ◽  
Circular Distributions ◽  
New Models ◽  
C Distribution

The Cardioid (C) distribution is one of the most important models for modeling circular data. Although some of its structural properties have been derived, this distribution is not appropriate for asymmetry and multimodal phenomena in the circle, and then extensions are required. There are various general methods that can be used to produce circular distributions. This paper proposes four extensions of the C distribution based on the beta, Kumaraswamy, gamma, and Marshall–Olkin generators. We obtain a unique linear representation of their densities and some mathematical properties. Inference procedures for the parameters are also investigated. We perform two applications on real data, where the new models are compared to the C distribution and one of its extensions.

scholarly journals Comparing two circular distributions: advice for effective implementation of statistical procedures in biology

2021 ◽  
Author(s):  
Lukas Landler ◽  
Graeme D Ruxton ◽  
Erich Pascal Malkemper
Keyword(s):  
Statistical Power ◽  
Type I Error ◽  
Statistical Treatment ◽  
Good Control ◽  
Time Of Day ◽  
Circular Data ◽  
Type I ◽  
Biological Variables ◽  
Circular Distributions ◽  
Two Samples

Many biological variables, often involving timings of events or directions, are recorded on a circular rather than linear scale, and need different statistical treatment for that reason. A common question that is asked of such circular data involves comparison between two groups or treatments: Are the populations from which the two samples drawn differently distributed around the circle? For example, we might ask whether the distribution of directions from which a stalking predator approaches its prey differs between sunny and cloudy conditions; or whether the time of day of mating attempts differs between lab mice subject to one of two hormone treatments. An array of statistical approaches to these questions have been developed. We compared 18 of these (by simulation) in terms of both abilities to control type I error rate near the nominal value, and statistical power. We found that only eight tests offered good control of type I error in all our test situations. Of these eight, we are able to identify Watsons U^2 test and MANOVA based on trigonometric functions of the data as offering the best power in the overwhelming majority of our test circumstances. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Hence, we recommend the routine use of either Watsons U^2 test or MANOVA when comparing two samples of circular data.

scholarly journals Wrapped Lomax Distribution :a New CircularProbability Model

2018 ◽  
Vol 7 (3.31) ◽  
pp. 150
Author(s):  
R Subba Rao ◽  
V Ravindranath ◽  
A V.Dattatreya Rao ◽  
G Prasad ◽  
P Ravi Kishore
Keyword(s):  
Medical Diagnosis ◽  
Queuing Theory ◽  
Life Time ◽  
Random Variable ◽  
Time Of Day ◽  
Circular Distribution ◽  
Lomax Distribution ◽  
Scale Parameters ◽  
Type Iv ◽  
Circular Model

Lomax Distribution (Pareto Type IV) is fitted for a life time random variable which can be studied for the data belongs to Actuarialscience, medical diagnosis and Queuing theory etc. In the time of day events observed in cycles like hourly, daily, weekly, monthlyor yearly are in circular distribution. By adopting the technique of wrapping an attempt is made to identify a new circular probabilitymodel originate as Wrapped Lomax Distribution. The concept of circular model is introduced and strategy of wrapping is given forLomaxDistribution. Wrapped Lomax Distribution PDF and CDF are derived, their graphs are also studied. The trigonometric momentsand characteristic function of Wrapped Lomax Distribution are obtained and their graphs are also depicted. The characteristics likemean, variance, skewness, kurtosis and circular standard deviation for various values of location and scale parameters are derived in this paper.  

Short- and long-range dispersal of the Queensland fruit fly, Bactrocera tryoni and its relevance to invasive potential, sterile insect technique and surveillance trapping

2008 ◽  
Vol 48 (9) ◽  
pp. 1237 ◽  
Author(s):  
A. Meats ◽  
J. E. Edgerton
Keyword(s):  
Sterile Insect Technique ◽  
Single Point ◽  
Cauchy Distribution ◽  
Fruit Fly ◽  
Bactrocera Tryoni ◽  
Scale Invariant ◽  
Long Distance ◽  
Negative Power ◽  
Catch Rates ◽  
Cauchy Model

Dispersal of immature and sexually mature Queensland fruit fly, Bactrocera tryoni (Froggatt) from releases made at a single point was assessed from recapture rates obtained by using arrays of traps. The recapture data (pertaining to distances up to 480 m) fitted both logarithmic and Cauchy models although the fits for the releases of immature flies were inferior because of high variability in catches at certain distances. When combined with data previously published for longer distances, a Cauchy model fitted data for releases of immature flies well and indicated that the median distance dispersed after emerging from the puparium was ~120 m and that 90% of flies would displace less than 800 m despite the fact that a consistent trend in declining catch rates can be obtained up to at least 85 km. This is consistent with the tail of the Cauchy distribution having a slope congruent with a negative power curve and thus being scale invariant for longer distances. The distribution of recaptured flies that were released as adults also fitted a Cauchy model with a tail of the same slope, suggesting that the spatial distribution of long-distance dispersers is not only scale invariant but also age invariant. This has significance to the ability of surveillance trapping arrays to detect infestations and also to methods of distributing insects for the sterile insect technique. Whereas the spread of invading propagules in the first generation is likely to be limited by a decline to non-viable density within 1 km or less of the incursion point, the influence of larger infestations on nearby uninfested regions would be limited by the longevity of the dispersers.

scholarly journals An IMM Filter Defined in the Linear-Circular Domain, Application to Maneuver Detection with Heading Only

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Karim El mokhtari ◽  
Serge Reboul ◽  
Georges Stienne ◽  
Jean Bernard Choquel ◽  
Benaissa Amami ◽  
...  
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Real Data ◽  
Circular Domain ◽  
Circular Data ◽  
Von Mises Distribution ◽  
A Posteriori ◽  
Circular Distributions ◽  
Vehicle Maneuver ◽  
Von Mises

In this article, we propose a multimodel filter for circular data. The so-called Circular Interacting Multimodel filter is derived in a Bayesian framework with the circular normal von Mises distribution. The aim of the proposed filter is to obtain the same performance in the circular domain as the classical IMM filter in the linear domain. In our approach, the mixing and fusion stages of the Circular Interacting Multimodel filter are, respectively, defined from the a priori and from the a posteriori circular distributions of the state angle knowing the measurements and according to a set of models. We propose in this article a set of circular models that will be used in order to detect the vehicle maneuvers from heading measurements. The Circular Interacting Multimodel filter performances are assessed on synthetic data and we show on real data a vehicle maneuver detection application.

Localization of Gallium-67 in Peritoneal Cells by Electron Microscopic Autoradiography

1973 ◽  
Vol 31 ◽  
pp. 404-405
Author(s):  
D. C. Swartzendruber ◽  
Norma L. Idoyaga-Vargas
Keyword(s):  
Clinical Trials ◽  
Soft Tissue ◽  
Tumor Tissue ◽  
Soft Tissue Tumors ◽  
Clinical Usefulness ◽  
Electron Microscopic ◽  
Normal Cells ◽  
Electron Microscopic Autoradiography ◽  
Peritoneal Cells ◽  
Gallium 67

The radionuclide gallium-67 (67Ga) localizes preferentially but not specifically in many human and experimental soft-tissue tumors. Because of this localization, 67Ga is used in clinical trials to detect humar. cancers by external scintiscanning methods. However, the fact that 67Ga does not localize specifically in tumors requires for its eventual clinical usefulness a fuller understanding of the mechanisms that control its deposition in both malignant and normal cells. We have previously reported that 67Ga localizes in lysosomal-like bodies, notably, although not exclusively, in macrophages of the spocytaneous AKR thymoma. Further studies on the uptake of 67Ga by macrophages are needed to determine whether there are factors related to malignancy that might alter the localization of 67Ga in these cells and thus provide clues to discovering the mechanism of 67Ga localization in tumor tissue.

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