Template:ParameterTypes - Revision history

Lisa Hacker: Redirected page to Life Distributions

2012-08-09T10:07:47Z

← Older revision		Revision as of 10:07, 9 August 2012
Line 1:		Line 1:
	[[~~Category: For Deletion~~]]		#REDIRECT [[Life_Distributions]]

Lisa Hacker: Replaced content with 'Category: For Deletion'

2012-07-20T12:13:18Z

Replaced content with 'Category: For Deletion'

← Older revision		Revision as of 12:13, 20 July 2012
Line 1:		Line 1:
	~~=== Parameter Types ===~~		[[Category: For Deletion]]

	Distributions can have any number of parameters. Do note that as the number of parameters increases, so does the amount of data required for a proper fit. In general, the lifetime distributions used for reliability and life data analysis are usually limited to a maximum of three parameters. These three parameters are usually known as the ''scale parameter'', the ''shape parameter'' and the ''location parameter''.

	~~'''Scale Parameter'''~~

	The scale parameter is the most common type of parameter. All distributions in this reference have a scale parameter. In the case of one-parameter distributions, the sole parameter is the scale parameter. The scale parameter defines where the bulk of the distribution lies, or how stretched out the distribution is. In the case of the normal distribution, the scale parameter is the standard deviation.

	~~'''Shape Parameter'''~~

	The shape parameter, as the name implies, helps define the shape of a distribution. Some distributions, such as the exponential or normal, do not have a shape parameter since they have a predefined shape that does not change. In the case of the normal distribution, the shape is always the familiar bell shape. The effect of the shape parameter on a distribution is reflected in the shapes of the <span class="texhtml">''pdf''</span>, the reliability function and the failure rate function.

	~~'''Location Parameter'''~~

	The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <span class="texhtml">γ</span>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.

	[[~~Image~~:~~locationparameter.png\|center\|200px]]~~

	This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <span class="texhtml">γ</span> can either be positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <span class="texhtml">γ</span>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping process. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.

	~~== Most Commonly Used Distributions ==~~

	~~There are many different lifetime distributions that can be used to model reliability data. Leemis and others [[Appendix:_Weibull_References\|[22]~~]] present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.

Nicolette Young: /* Parameter Types */

2012-04-25T16:44:34Z

Parameter Types

← Older revision		Revision as of 16:44, 25 April 2012
Line 15:		Line 15:
	The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <span class="texhtml">γ</span>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.		The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <span class="texhtml">γ</span>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.

	[[Image:locationparameter.png\|center\|~~400px~~]]		[[Image:locationparameter.png\|center\|200px]]

	This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <span class="texhtml">γ</span> can either be positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <span class="texhtml">γ</span>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping process. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.		This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <span class="texhtml">γ</span> can either be positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <span class="texhtml">γ</span>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping process. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.

Lisa Hacker: /* Parameter Types */

2012-03-30T21:50:05Z

Parameter Types

← Older revision		Revision as of 21:50, 30 March 2012
Line 3:		Line 3:
	Distributions can have any number of parameters. Do note that as the number of parameters increases, so does the amount of data required for a proper fit. In general, the lifetime distributions used for reliability and life data analysis are usually limited to a maximum of three parameters. These three parameters are usually known as the ''scale parameter'', the ''shape parameter'' and the ''location parameter''.		Distributions can have any number of parameters. Do note that as the number of parameters increases, so does the amount of data required for a proper fit. In general, the lifetime distributions used for reliability and life data analysis are usually limited to a maximum of three parameters. These three parameters are usually known as the ''scale parameter'', the ''shape parameter'' and the ''location parameter''.

	~~====~~ Scale Parameter ~~====~~		'''Scale Parameter'''

	The scale parameter is the most common type of parameter. All distributions in this reference have a scale parameter. In the case of one-parameter distributions, the sole parameter is the scale parameter. The scale parameter defines where the bulk of the distribution lies, or how stretched out the distribution is. In the case of the normal distribution, the scale parameter is the standard deviation.		The scale parameter is the most common type of parameter. All distributions in this reference have a scale parameter. In the case of one-parameter distributions, the sole parameter is the scale parameter. The scale parameter defines where the bulk of the distribution lies, or how stretched out the distribution is. In the case of the normal distribution, the scale parameter is the standard deviation.

	~~====~~ Shape Parameter ~~====~~		'''Shape Parameter'''

	The shape parameter, as the name implies, helps define the shape of a distribution. Some distributions, such as the exponential or normal, do not have a shape parameter since they have a predefined shape that does not change. In the case of the normal distribution, the shape is always the familiar bell shape. The effect of the shape parameter on a distribution is reflected in the shapes of the <span class="texhtml">''pdf''</span>, the reliability function and the failure rate function.		The shape parameter, as the name implies, helps define the shape of a distribution. Some distributions, such as the exponential or normal, do not have a shape parameter since they have a predefined shape that does not change. In the case of the normal distribution, the shape is always the familiar bell shape. The effect of the shape parameter on a distribution is reflected in the shapes of the <span class="texhtml">''pdf''</span>, the reliability function and the failure rate function.

	~~====~~ Location Parameter ~~====~~		'''Location Parameter'''

	The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <span class="texhtml">γ</span>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.		The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <span class="texhtml">γ</span>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.

Nicolette Young: /* Location Parameter */

2012-03-12T17:21:08Z

Location Parameter

← Older revision		Revision as of 17:21, 12 March 2012
Line 15:		Line 15:
	The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <span class="texhtml">γ</span>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.		The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <span class="texhtml">γ</span>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.

	[[Image:~~Gamma~~.~~gif\|thumb~~\|center\|~~200px~~]]		[[Image:locationparameter.png\|center\|400px]]

	This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <span class="texhtml">γ</span> can either be positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <span class="texhtml">γ</span>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping process. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.		This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <span class="texhtml">γ</span> can either be positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <span class="texhtml">γ</span>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping process. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.

Kate Racaza at 15:56, 12 March 2012

2012-03-12T15:56:22Z

← Older revision		Revision as of 15:56, 12 March 2012
Line 21:		Line 21:
	== Most Commonly Used Distributions ==		== Most Commonly Used Distributions ==

	There are many different lifetime distributions that can be used to model reliability data. Leemis and others [[Appendix E: ~~Weibull References~~\|[22]]] present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.		There are many different lifetime distributions that can be used to model reliability data. Leemis and others [[Appendix:_Weibull_References\|[22]]] present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.

Kate Racaza at 15:55, 12 March 2012

2012-03-12T15:55:04Z

← Older revision		Revision as of 15:55, 12 March 2012
Line 19:		Line 19:
	This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <span class="texhtml">γ</span> can either be positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <span class="texhtml">γ</span>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping process. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.		This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <span class="texhtml">γ</span> can either be positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <span class="texhtml">γ</span>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping process. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.

	==Most Commonly Used Distributions==		== Most Commonly Used Distributions ==
	There are many different lifetime distributions that can be used to model reliability data. [[Appendix E: Weibull References \| ~~Leemis~~ [22]]] ~~and others~~ present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.
			There are many different lifetime distributions that can be used to model reliability data. Leemis and others [[Appendix E: Weibull References\|[22]]] present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.

Kate Racaza at 15:53, 12 March 2012

2012-03-12T15:53:30Z

← Older revision		Revision as of 15:53, 12 March 2012
Line 1:		Line 1:
	===Parameter Types===		=== Parameter Types ===
	Distributions can have any number of parameters. Do note that as the number of parameters increases, so does the amount of data required for a proper fit. In general, most distributions used for reliability and life data analysis, the lifetime distributions, usually are limited to a maximum of three parameters. These three parameters are usually known as the ''scale parameter'', the ''shape parameter'' and the ''location parameter''.

	~~====Scale Parameter====~~		Distributions can have any number of parameters. Do note that as the number of parameters increases, so does the amount of data required for a proper fit. In general, the lifetime distributions used for reliability and life data analysis are usually limited to a maximum of three parameters. These three parameters are usually known as the ''scale parameter'', the ''shape parameter'' and the ''location parameter''.
	~~The scale parameter is the most common type~~ of ~~parameter~~. ~~All distributions in this reference have a scale parameter. In~~ the ~~case~~ of ~~one-parameter distributions~~, the ~~sole parameter is the scale parameter. The scale parameter defines where the bulk~~ of ~~the distribution lies, or how stretched out the distribution is~~. In the ~~case~~ of the ~~normal distribution~~, the ~~scale~~ parameter is the ~~standard deviation~~.

	====~~Shape~~ Parameter====		==== Scale Parameter ====
	The shape parameter, as the name implies, helps define the shape of a distribution. Some distributions, such as the exponential or normal, do not have a shape parameter since they have a predefined shape that does not change. In the case of the normal distribution, the shape is always the familiar bell shape. The effect of the shape parameter on a distribution is reflected in the shapes of the <math>pdf</math>, the reliability function and the failure rate function.

	~~====Location Parameter====~~		The scale parameter is the most common type of parameter. All distributions in this reference have a scale parameter. In the case of one-parameter distributions, the sole parameter is the scale parameter. The scale parameter defines where the bulk of the distribution lies, or how stretched out the distribution is. In the case of the normal distribution, the scale parameter is the standard deviation.
	The ~~location~~ parameter is ~~used to shift~~ a ~~distribution in~~ one ~~direction or another~~. The ~~location~~ parameter~~, usually denoted as <math>\gamma </math>,~~ defines the ~~location~~ of the ~~origin of a~~ distribution ~~and can be either positive~~ or ~~negative~~. In ~~terms~~ of ~~lifetime distributions~~, the ~~location~~ parameter ~~represents a time shift~~.

	~~[[Image:gamma.gif\|thumb\|center\|800px\|Graphical view of the location parameter]]~~

	This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <~~math~~>~~\gamma~~ </~~math~~> can be ~~either~~ positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <~~math~~>~~\gamma~~ </~~math~~>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping ~~processes~~. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.		==== Shape Parameter ====

			The shape parameter, as the name implies, helps define the shape of a distribution. Some distributions, such as the exponential or normal, do not have a shape parameter since they have a predefined shape that does not change. In the case of the normal distribution, the shape is always the familiar bell shape. The effect of the shape parameter on a distribution is reflected in the shapes of the <span class="texhtml">''pdf''</span>, the reliability function and the failure rate function.

			==== Location Parameter ====

			The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <span class="texhtml">γ</span>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.

			[[Image:Gamma.gif\|thumb\|center\|200px]]

			This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <span class="texhtml">γ</span> can either be positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <span class="texhtml">γ</span>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping process. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.

	==Most Commonly Used Distributions==		==Most Commonly Used Distributions==
	There are many different lifetime distributions that can be used to model reliability data. [[Appendix E: Weibull References \| Leemis [22]]] and others present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.		There are many different lifetime distributions that can be used to model reliability data. [[Appendix E: Weibull References \| Leemis [22]]] and others present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.

Harry Guo: /* Most Commonly Used Distributions */

2012-02-03T23:09:01Z

Most Commonly Used Distributions

← Older revision		Revision as of 23:09, 3 February 2012
Line 16:		Line 16:

	==Most Commonly Used Distributions==		==Most Commonly Used Distributions==
	There are many different lifetime distributions that can be used to model reliability data. Leemis [22] and others present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.		There are many different lifetime distributions that can be used to model reliability data. [[Appendix E: Weibull References \| Leemis [22]]] and others present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.

Nicolette Young: Created page with '===Parameter Types=== Distributions can have any number of parameters. Do note that as the number of parameters increases, so does the amount of data required for a proper fit. I…'

2012-01-03T23:05:45Z

Created page with '===Parameter Types=== Distributions can have any number of parameters. Do note that as the number of parameters increases, so does the amount of data required for a proper fit. I…'

New page

===Parameter Types===
Distributions can have any number of parameters. Do note that as the number of parameters increases, so does the amount of data required for a proper fit. In general, most distributions used for reliability and life data analysis, the lifetime distributions, usually are limited to a maximum of three parameters. These three parameters are usually known as the ''scale parameter'', the ''shape parameter'' and the ''location parameter''.

====Scale Parameter====
The scale parameter is the most common type of parameter. All distributions in this reference have a scale parameter. In the case of one-parameter distributions, the sole parameter is the scale parameter. The scale parameter defines where the bulk of the distribution lies, or how stretched out the distribution is. In the case of the normal distribution, the scale parameter is the standard deviation.

====Shape Parameter====
The shape parameter, as the name implies, helps define the shape of a distribution. Some distributions, such as the exponential or normal, do not have a shape parameter since they have a predefined shape that does not change. In the case of the normal distribution, the shape is always the familiar bell shape. The effect of the shape parameter on a distribution is reflected in the shapes of the <math>pdf</math>, the reliability function and the failure rate function.

====Location Parameter====
The location parameter is used to shift a distribution in one direction or another. The location parameter, usually denoted as <math>\gamma </math>, defines the location of the origin of a distribution and can be either positive or negative. In terms of lifetime distributions, the location parameter represents a time shift.

[[Image:gamma.gif|thumb|center|800px|Graphical view of the location parameter]]

This means that the inclusion of a location parameter for a distribution whose domain is normally <math>[0,\infty]</math> will change the domain to <math>[\gamma ,\infty]</math> , where <math>\gamma </math> can be either positive or negative. This can have some profound effects in terms of reliability. For a positive location parameter, this indicates that the reliability for that particular distribution is always 100% up to that point. In other words, a failure cannot occur before this time <math>\gamma </math>. Many engineers feel uncomfortable in saying that a failure will absolutely not happen before any given time. On the other hand, the argument can be made that almost all life distributions have a location parameter, although many of them may be negligibly small. Similarly, many people are uncomfortable with the concept of a negative location parameter, which states that failures theoretically occur before time zero. Realistically, the calculation of a negative location parameter is indicative of quiescent failures (failures that occur before a product is used for the first time) or of problems with the manufacturing, packaging or shipping processes. More attention will be given to the concept of the location parameter in subsequent discussions of the exponential and Weibull distributions, which are the lifetime distributions that most frequently employ the location parameter.

==Most Commonly Used Distributions==
There are many different lifetime distributions that can be used to model reliability data. Leemis [22] and others present a good overview of many of these distributions. In this reference, we will concentrate on the most commonly used and most widely applicable distributions for life data analysis, as outlined in the following sections.