Estimating the home range

1994 ◽  
Vol 31 (03) ◽  
pp. 700-720 ◽  
Author(s):  
L. De Haan ◽  
Sidney Resnick
Keyword(s):  
Continuous Function ◽  
Home Range ◽  
Confidence Region ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Polar Coordinates ◽  
Common Distribution ◽  
The Right ◽  
The Given ◽  
Independent Identically Distributed

A proposal is given for estimating the home range of an animal based on sequential sightings. We assume the given sightings are independent, identically distributed random vectors X 1,· ··, Xn whose common distribution has compact support. If are the polar coordinates of the sightings, then is a sup-measure and corresponds to the right endpoint of the distribution . The corresponding upper semi-continuous function l(θ) is the boundary of the home range. We give a consistent estimator for the boundary l and under the assumption that the distribution of R 1 given is in the domain of attraction of an extreme value distribution with bounded support, we are able to give an approximate confidence region.

Estimating the home range

1994 ◽  
Vol 31 (3) ◽  
pp. 700-720 ◽  
Author(s):  
L. De Haan ◽  
Sidney Resnick
Keyword(s):  
Continuous Function ◽  
Home Range ◽  
Confidence Region ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Polar Coordinates ◽  
Common Distribution ◽  
The Right ◽  
The Given ◽  
Independent Identically Distributed

A proposal is given for estimating the home range of an animal based on sequential sightings. We assume the given sightings are independent, identically distributed random vectors X1,· ··, Xn whose common distribution has compact support. If are the polar coordinates of the sightings, then is a sup-measure and corresponds to the right endpoint of the distribution . The corresponding upper semi-continuous function l(θ) is the boundary of the home range. We give a consistent estimator for the boundary l and under the assumption that the distribution of R1 given is in the domain of attraction of an extreme value distribution with bounded support, we are able to give an approximate confidence region.

A note on a condition satisfied by certain random walks

1977 ◽  
Vol 14 (04) ◽  
pp. 843-849 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Final Section ◽  
Domain Of Attraction ◽  
Partial Result ◽  
Stable Law ◽  
Left Hand ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Image Position ◽  
The Right ◽  
Necessary And Sufficient

The problem considered is to elucidate under what circumstances the condition holds, where and Xi are independent and have common distribution function F. The main result is that if F has zero mean, and (*) holds with F belongs to the domain of attraction of a completely asymmetric stable law of parameter 1/γ. The cases are also treated. (The case cannot arise in these circumstances.) A partial result is also given for the case when and the right-hand tail is ‘asymptotically larger’ than the left-hand tail. For 0 < γ < 1, (*) is known to be a necessary and sufficient condition for the arc-sine theorem to hold for Nn , the number of positive terms in (S 1, S 2, …, Sn ). In the final section we point out that in the case γ = 1 a limit theorem of a rather peculiar type can hold for Nn.

scholarly journals Extreme values of an infinite mixture of normally distributed variables

Filomat ◽  
2013 ◽  
Vol 27 (5) ◽  
pp. 909-916
Author(s):  
Ehfayed Shneina ◽  
Vladimir Bozin
Keyword(s):  
Distribution Function ◽  
Extreme Values ◽  
Infinite Sequence ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Value Distribution ◽  
Common Distribution ◽  
Common Distribution Function ◽  
The Common ◽  
Normally Distributed

We study distribution of extreme values of a mixture of an infinite sequence of independent normally distributed variables with the same mean and an increasing sequence of standard deviations, and prove that the common distribution function belongs to the domain of attraction of Gumbel extreme value distribution. The norming constants for the maximum also are given.

Tail equivalence and its applications

1971 ◽  
Vol 8 (01) ◽  
pp. 136-156 ◽  
Author(s):  
Sidney I. Resnick
Keyword(s):  
Markov Chain ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Distribution Functions ◽  
Value Distribution ◽  
Normalizing Constants ◽  
Independent Identically Distributed

If for two c.d.f.'s F(·) and G(·), 1 – F(x)/1 – G(x) → A, 0 <A <∞ , as x → ∞, then for normalizing constants an > 0, bn, n > 1, Fn (anx + bn ) → φ(x), φ(x) non-degenerate, iff Gn (anx + bn )→ φ A−1(x). Conversely, if Fn (anx+bn )→ φ(x), Gn (anx + bn ) → φ'(x), φ(x) and φ'(x) non-degenerate, then there exist constants C >0 and D such that φ'(x) =φ(Cx + D) and limx→∞ 1 — F(x)/1 — G(x) exists and is expressed in terms of C and D, depending on which type of extreme value distribution φ(x) is. These results are used to study domain of attraction questions for products of distribution functions and to reduce the limit law problem for maxima of a sequence of random variables defined on a Markov chain (M.C.) to the independent, identically distributed (i.i.d.) case.

A note on a condition satisfied by certain random walks

1977 ◽  
Vol 14 (4) ◽  
pp. 843-849 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Final Section ◽  
Domain Of Attraction ◽  
Partial Result ◽  
Stable Law ◽  
Left Hand ◽  
Common Distribution ◽  
Common Distribution Function ◽  
Image Position ◽  
The Right ◽  
Necessary And Sufficient

The problem considered is to elucidate under what circumstances the condition holds, where and Xi are independent and have common distribution function F. The main result is that if F has zero mean, and (*) holds with F belongs to the domain of attraction of a completely asymmetric stable law of parameter 1/γ. The cases are also treated. (The case cannot arise in these circumstances.) A partial result is also given for the case when and the right-hand tail is ‘asymptotically larger’ than the left-hand tail. For 0 < γ < 1, (*) is known to be a necessary and sufficient condition for the arc-sine theorem to hold for Nn, the number of positive terms in (S1, S2, …, Sn). In the final section we point out that in the case γ = 1 a limit theorem of a rather peculiar type can hold for Nn.

Tail equivalence and its applications

1971 ◽  
Vol 8 (1) ◽  
pp. 136-156 ◽  
Author(s):  
Sidney I. Resnick
Keyword(s):  
Markov Chain ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Extreme Value Distribution ◽  
Extreme Value ◽  
Distribution Functions ◽  
Value Distribution ◽  
Normalizing Constants ◽  
Independent Identically Distributed

If for two c.d.f.'s F(·) and G(·), 1 – F(x)/1 – G(x) → A, 0 <A <∞, as x → ∞, then for normalizing constants an > 0, bn, n > 1, Fn(anx + bn) → φ(x), φ(x) non-degenerate, iff Gn(anx + bn)→ φ A−1(x). Conversely, if Fn(anx+bn)→ φ(x), Gn(anx + bn) → φ'(x), φ(x) and φ'(x) non-degenerate, then there exist constants C >0 and D such that φ'(x) =φ(Cx + D) and limx→∞ 1 — F(x)/1 — G(x) exists and is expressed in terms of C and D, depending on which type of extreme value distribution φ(x) is. These results are used to study domain of attraction questions for products of distribution functions and to reduce the limit law problem for maxima of a sequence of random variables defined on a Markov chain (M.C.) to the independent, identically distributed (i.i.d.) case.

Manufacturability Analysis for Solid Freeform Fabrication

1999 ◽  
Author(s):  
R. K. Arni ◽  
S. K. Gupta
Keyword(s):  
Systematic Approach ◽  
Solid Freeform Fabrication ◽  
Second Step ◽  
Freeform Fabrication ◽  
Design Tolerance ◽  
The Face ◽  
The Right ◽  
The Given ◽  
Manufacturing Problems ◽  
Case Effect

Abstract This paper describes a systematic approach to analyzing manufacturability of parts produced using Solid Freeform Fabrication (SFF) processes with flatness, parallelism and perpendicularity tolerance requirements on the planar faces of the part. SFF processes approximate objects using layers, therefore the part being produced exhibits stair-case effect. The extent of this stair-case effect depends on the angle between the build orientation and the face normal. Therefore, different faces whose direction normal is oriented differently with respect to the build direction may exhibit different values of inaccuracies. We use a two step approach to perform the manufacturability analysis. We first analyze each specified tolerance on the part and identify the set of feasible build directions that can be used to satisfy that tolerance. As a second step, we take the intersection of all sets of feasible build directions to identify the set of build directions that can simultaneously satisfy all specified tolerance requirements. If there is at least one build direction that can satisfy all tolerance requirements, then the part is considered manufacturable. Otherwise, the part is considered non-manufacturable. Our research will help SFF designers and process providers in the following ways. By evaluating design tolerances against a given process capability, it will help designers in eliminating manufacturing problems and selecting the right SFF process for the given design. It will help process providers in selecting a build direction that can meet all design tolerance requirements.

scholarly journals Resolvent of nonautonomous linear delay functional differential equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Joël Blot ◽  
Mamadou I. Koné
Keyword(s):  
Continuous Function ◽  
Differential Equations ◽  
Differentiable Function ◽  
Functional Differential Equations ◽  
Initial Value ◽  
Complete Proof ◽  
Right Hand ◽  
Linear Delay ◽  
Functional Differential ◽  
The Right

AbstractThe aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

scholarly journals OSOBENNOSTI POKAZATELEY UL'TRASONOMETRII ZhENSKOGO NASELENIYa GORODA ChELYaBINSKA

2005 ◽  
Vol 8 (2) ◽  
pp. 25-28
Author(s):  
E N USOL'TsEVA ◽  
O V SAFRONOV ◽  
E V BRYuKhINA
Keyword(s):  
Characteristic Feature ◽  
Ultrasound Wave ◽  
Spongy Bone ◽  
Anatomic Structure ◽  
Lower Jaw ◽  
Tibia Diaphysis ◽  
The Right ◽  
The Given ◽  
Peripheral Skeleton ◽  
Tubular Bones

Characteristic feature of ultrasonic densitometry have been investigated in women,s population of Chelyabinsk (n=200) from 25 to 65 years old. We used domestically produced Echoosteometr-02. A basis of a body of the lower jaw became a new area for ultrasonic densitometry. We can recommend a lower jaw as a new area for ultrasonic densitometry taking into account high pithiness of data in a combination with simplicity of research. Traditional localizations have been also applied: proximal phalanges of the hand, patella, tibia diaphysis and calcaneus bones of the right and left sides. We have established a "peak" values of a speed of the ultrasound wave for the given bones. Also we have found that a tubular bones and a large spongy bone - a lower jaw - possess the highest speed of an ultrasound wave, and the speed was mach less in a small spongy bones, that is caused by their anatomic structure. Ultrasound densitometry parameters of the peripheral skeleton start to reduce from 40-50 years behind exception patella - from 55 years. The lowest values were in group of women of 60-65 years. The rates of ultrasonic densitometry received by us are possible to use for women population of Chelyabinsk.

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