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en>Melcous: /* Companies */ no wiki page = not needed on disambig page

2015-01-05T12:31:22Z

Companies: no wiki page = not needed on disambig page

← Older revision		Revision as of 14:31, 5 January 2015
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	~~The writer's~~ title is ~~Andera and she thinks~~ it ~~seems fairly great. Ohio~~ is ~~exactly where~~ my ~~home~~ is ~~love psychic ([http://Cartoonkorea.com/ce002/1093612 Cartoonkorea.com]) but my spouse desires us~~ to ~~transfer~~. ~~One of~~ the ~~things she enjoys most~~ is ~~canoeing and she~~'~~s been performing it for fairly a while. [http://203~~.~~250.78.160/zbxe/?document_srl=1792908 phone psychic readings] He is an order clerk and it~~'~~s something he really appreciate~~.<br><br>~~Also visit~~ my ~~web-site :: free psychic -~~ [http://~~formalarmour~~.~~com/index~~.~~php?do=/profile-26947/info/ http:~~/~~/formalarmour.com~~/index.php?do=~~/profile-26947/info~~] -		Hi there. My title is Sophia Meagher although it is not the title on my beginning certificate. Credit authorising is how she tends to make a living. My husband doesn't like it the way I do but what I really like performing is caving but I don't have the time lately. I've always loved living in Alaska.<br><br>my website ... [http://c045.danah.co.kr/home/index.php?document_srl=1356970&mid=qna psychic readings]

en>Bkonrad: already listed

2014-02-25T01:01:23Z

already listed

← Older revision		Revision as of 03:01, 25 February 2014
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	~~In [[actuarial science]],~~ '~~''force of mortality''' represents the instantaneous [[Mortality rate\|rate of mortality]] at a certain age measured on an annualized basis. It~~ is ~~identical in concept to [[failure rate]], also called [[hazard function]], in [[reliability theory]].~~		The writer's title is Andera and she thinks it seems fairly great. Ohio is exactly where my home is love psychic ([http://Cartoonkorea.com/ce002/1093612 Cartoonkorea.com]) but my spouse desires us to transfer. One of the things she enjoys most is canoeing and she's been performing it for fairly a while. [http://203.250.78.160/zbxe/?document_srl=1792908 phone psychic readings] He is an order clerk and it's something he really appreciate.<br><br>Also visit my web-site :: free psychic - [http://formalarmour.com/index.php?do=/profile-26947/info/ http://formalarmour.com/index.php?do=/profile-26947/info] -

	~~==Motivation~~ and ~~definition==~~

	~~In a [[life table]], we consider the probability of a person dying from age ''x'' to ''x'' + 1, called ''q''<sub>''x''</sub>~~. ~~In the continuous case, we could also consider the [[conditional probability]] of a person who has attained age (''x'') dying between ages ''x'' and ''x'' + ''Δx'', which~~ is

	~~:<math>P_{x}(\Delta x)=P(x<X<x+\Delta\;x\mid\;X>x)=\frac{F_X(x+\Delta\;x)-F_X(x)}{(1-F_X(x))}</math>~~

	where ~~F<sub>X</sub>~~(~~x) is the~~ [[distribution function]] of the continuous age-at-death [[random variable]], X. As ''Δx'' tends to zero, so does this probability in the continuous case. The approximate force of mortality is this probability divided by ''Δx''. If we let ''Δx'' tend to zero, we get the function for '''force of mortality''', denoted by <math>\mu(x)</math>:

	~~:<math>\mu\,(x)=\frac{F'_X(x)}{1-F_X(x)}<~~/~~math>~~

	~~Since ''f''<sub>''X''<~~/~~sub>(''x'')=''F'' '<sub>''X''<~~/~~sub>(''x'') is the probability density function of ''X'', and ''S''(''x'') = 1 - ''F''<sub>''X''<~~/~~sub>(''x'') is the [[survival function~~]~~], the force of mortality can also be expressed variously as:~~

	~~:<math>\mu\,(x~~)~~=\frac{f_X(x)}{1-F_X(x)}=-\frac{S'(x)}{S(x)}=-{\frac{d}{dx}}ln[S(x)]~~.~~</math>~~

	To understand conceptually how the force of mortality operates within a population, consider that the ages, ''x'', where the probability density function ''f''<sub>''X''</sub>(''x'') is zero, there is no chance of ~~dying. Thus~~ the ~~force of mortality at these ages~~ is ~~zero.~~

	~~The force of mortality <math>\mu(x)</math> can be interpreted as the~~ '~~'conditional'' density of failure at age ''x'',~~ while ~~''f''(''x'') is the ''unconditional'' density of failure at age ''x''~~.~~<ref name=MQR>R~~. ~~Cunningham, T~~. ~~Herzog, R~~. ~~London (2008). ''Models for Quantifying Risk, 3rd Edition'', Actex.<~~/~~ref> The unconditional density of failure at age ''x''~~ is ~~the product of the probability of survival to age ''x'',~~ and ~~the conditional density of failure at age ''x'', given survival to age ''x'~~'.

	~~This is expressed in symbols as~~

	:<~~math~~>~~\,\mu(x)S(x) = f_X(x)~~<~~/math~~>

	~~or equivalently~~

	:~~<math>\mu(x) = \frac{f_X(x)}{S(x)}.</math>~~

	In many instances, it is also desirable to determine the survival probability function when the force of mortality is known. To do this, integrate the force of mortality over the interval ''x'' to ''x + t''

	:~~<math> \int_{x}^{x+t}~~ -~~\frac{d}{dy} ln~~[~~S(y)]\, dy </math>.~~

	~~By the fundamental theorem of calculus, this is simply~~

	:~~<math> ln[S(x + t)] - ln[S(x)], <~~/~~math>~~

	~~and taking the exponent to the base ''e'' results in~~

	~~:<math> \frac{S(x+t)}{S(x)} = S(t). <~~/~~math>~~

	~~Therefore, the survival probability of an individual of age ''x'' is written in terms of the force of mortality as~~

	~~:<math> S_x(t) = e^{-\int_x^{x+t}\mu(y)\, dy\,}~~. </~~math>~~

	~~==Examples==~~

	~~This example is taken from~~.<ref>Dickson, David C.M., Cambridge (2009). ''Actuarial Mathematics for Life Contingent Risks, First Edition'', Cambridge University Press.</ref> A survival model follows Makeham's law if the force of mortality is

	~~:<math>\mu(y)~~ = ~~A + Bc^{y} \quad\text{for } y \geqslant 0.<~~/~~math>~~

	~~Using the last formula, we have~~

	~~:<math>\int_x^{x+t} A + Bc^{y} dy = At + B(c^{x+t}~~-~~c^{x})~~/~~ln[c].<~~/~~math>~~

	~~Then~~

	~~:<math>S_x(t) = e^{-(At + B(c^{x+t}-c^{x})/ln[c])} = e^{-At} g^{c^{x} (c^{t}-1)} </math>~~

	~~where <math>g=e^{-B/ln[c]}.</math>~~

	~~== See also ==~~
	* [[Failure rate]]
	* [[Hazard function]]
	* [[Actuarial present value]]
	* [[Actuarial science]]
	* [[Reliability theory]]

	~~== References ==~~
	~~{{Reflist}}~~

	~~==External links==~~
	*http://~~www.fenews~~.com/~~fen46~~/~~topics_act_analysis~~/~~topics~~-~~act-analysis.htm~~

	~~[[Category:Actuarial science]]~~
	~~[[Category:Demography]]~~

en>Joe Schmedley: /* Entertainment */ oops

2014-01-05T00:48:36Z

Entertainment: oops

← Older revision		Revision as of 02:48, 5 January 2014
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	~~Alyson~~ is the ~~name individuals use~~ to ~~call me and I think it seems fairly great when you say it~~. ~~For~~ a ~~while I~~'~~ve [http~~://~~www~~.~~sirudang~~.~~com~~/~~siroo_Notice~~/~~2110 psychic chat online~~] ~~been in Alaska but accurate psychic predictions~~ ([~~http:~~//~~ustanford~~.~~com~~/~~index~~.~~php?do~~=/~~profile~~-~~38218~~/~~info/ ustanford~~.~~com~~]) ~~I will have~~ to ~~move~~ in ~~a yr or two~~. ~~Since I was eighteen I~~'~~ve been working~~ as ~~a bookkeeper but quickly my spouse and I will start our own business~~. ~~She~~ is ~~really fond~~ of ~~caving but she doesn'~~t ~~have the time lately~~.<br><br>~~My homepage~~ - ~~clairvoyance~~ ([http://~~afeen~~.~~fbho~~.~~net~~/v2/~~index.php?do=~~/~~profile~~-~~210/info/ afeen~~.~~fbho.net~~])		In [[actuarial science]], '''force of mortality''' represents the instantaneous [[Mortality rate\|rate of mortality]] at a certain age measured on an annualized basis. It is identical in concept to [[failure rate]], also called [[hazard function]], in [[reliability theory]].

			==Motivation and definition==

			In a [[life table]], we consider the probability of a person dying from age ''x'' to ''x'' + 1, called ''q''<sub>''x''</sub>. In the continuous case, we could also consider the [[conditional probability]] of a person who has attained age (''x'') dying between ages ''x'' and ''x'' + ''Δx'', which is

			:<math>P_{x}(\Delta x)=P(x<X<x+\Delta\;x\mid\;X>x)=\frac{F_X(x+\Delta\;x)-F_X(x)}{(1-F_X(x))}</math>

			where F<sub>X</sub>(x) is the [[distribution function]] of the continuous age-at-death [[random variable]], X. As ''Δx'' tends to zero, so does this probability in the continuous case. The approximate force of mortality is this probability divided by ''Δx''. If we let ''Δx'' tend to zero, we get the function for '''force of mortality''', denoted by <math>\mu(x)</math>:

			:<math>\mu\,(x)=\frac{F'_X(x)}{1-F_X(x)}</math>

			Since ''f''<sub>''X''</sub>(''x'')=''F'' '<sub>''X''</sub>(''x'') is the probability density function of ''X'', and ''S''(''x'') = 1 - ''F''<sub>''X''</sub>(''x'') is the [[survival function]], the force of mortality can also be expressed variously as:

			:<math>\mu\,(x)=\frac{f_X(x)}{1-F_X(x)}=-\frac{S'(x)}{S(x)}=-{\frac{d}{dx}}ln[S(x)].</math>

			To understand conceptually how the force of mortality operates within a population, consider that the ages, ''x'', where the probability density function ''f''<sub>''X''</sub>(''x'') is zero, there is no chance of dying. Thus the force of mortality at these ages is zero.

			The force of mortality <math>\mu(x)</math> can be interpreted as the ''conditional'' density of failure at age ''x'', while ''f''(''x'') is the ''unconditional'' density of failure at age ''x''.<ref name=MQR>R. Cunningham, T. Herzog, R. London (2008). ''Models for Quantifying Risk, 3rd Edition'', Actex.</ref> The unconditional density of failure at age ''x'' is the product of the probability of survival to age ''x'', and the conditional density of failure at age ''x'', given survival to age ''x''.

			This is expressed in symbols as

			:<math>\,\mu(x)S(x) = f_X(x)</math>

			or equivalently

			:<math>\mu(x) = \frac{f_X(x)}{S(x)}.</math>

			In many instances, it is also desirable to determine the survival probability function when the force of mortality is known. To do this, integrate the force of mortality over the interval ''x'' to ''x + t''

			:<math> \int_{x}^{x+t} -\frac{d}{dy} ln[S(y)]\, dy </math>.

			By the fundamental theorem of calculus, this is simply

			:<math> ln[S(x + t)] - ln[S(x)], </math>

			and taking the exponent to the base ''e'' results in

			:<math> \frac{S(x+t)}{S(x)} = S(t). </math>

			Therefore, the survival probability of an individual of age ''x'' is written in terms of the force of mortality as

			:<math> S_x(t) = e^{-\int_x^{x+t}\mu(y)\, dy\,}. </math>

			==Examples==

			This example is taken from.<ref>Dickson, David C.M., Cambridge (2009). ''Actuarial Mathematics for Life Contingent Risks, First Edition'', Cambridge University Press.</ref> A survival model follows Makeham's law if the force of mortality is

			:<math>\mu(y) = A + Bc^{y} \quad\text{for } y \geqslant 0.</math>

			Using the last formula, we have

			:<math>\int_x^{x+t} A + Bc^{y} dy = At + B(c^{x+t}-c^{x})/ln[c].</math>

			Then

			:<math>S_x(t) = e^{-(At + B(c^{x+t}-c^{x})/ln[c])} = e^{-At} g^{c^{x} (c^{t}-1)} </math>

			where <math>g=e^{-B/ln[c]}.</math>

			== See also ==
			* [[Failure rate]]
			* [[Hazard function]]
			* [[Actuarial present value]]
			* [[Actuarial science]]
			* [[Reliability theory]]

			== References ==
			{{Reflist}}

			==External links==
			*http://www.fenews.com/fen46/topics_act_analysis/topics-act-analysis.htm

			[[Category:Actuarial science]]
			[[Category:Demography]]

en>Arsenikk: /* Organizations */ dab

2012-08-18T18:12:27Z

Organizations: dab

New page

Alyson is the name individuals use to call me and I think it seems fairly great when you say it. For a while I've [http://www.sirudang.com/siroo_Notice/2110 psychic chat online] been in Alaska but accurate psychic predictions ([http://ustanford.com/index.php?do=/profile-38218/info/ ustanford.com]) I will have to move in a yr or two. Since I was eighteen I've been working as a bookkeeper but quickly my spouse and I will start our own business. She is really fond of caving but she doesn't have the time lately.<br><br>My homepage - clairvoyance ([http://afeen.fbho.net/v2/index.php?do=/profile-210/info/ afeen.fbho.net])