Alternative heavy right tailed distribution to exponential distribution












1












$begingroup$


I have data whose distribution resembles an exponential distribution, but the data has a heavier tail than the exponential distribution.



I will be very glad for any recommendation of an alternative to the exponential distribution for the data.






exponential







share|cite|improve this question











$endgroup$








  • 3




    $begingroup$
    A good basis for any such recommendation is a theory about the underlying process, because tail estimation can be highly uncertain without having a large amount of data. What additional information can you supply about your problem?
    $endgroup$
    – whuber♦
    2 days ago










  • $begingroup$
    @whuber , data is about the time duration(in months) between car accidents day and reporting day of accidents. But I dont have so much data. It seems that, most of the accidents are generally being reported quickly, but some of the accidents are being reported lately. when, I fit the data with an exponantial distribution, I see that the tail seems so light compared with the data.
    $endgroup$
    – oercim
    2 days ago












  • $begingroup$
    One might suppose there is a statute of limitations or insurance limit, most likely a whole number of years. This wouldn't be modeled well by any standard heavy-tailed distribution. You ought to closely examine what data you do have.
    $endgroup$
    – whuber♦
    2 days ago
















1












$begingroup$


I have data whose distribution resembles an exponential distribution, but the data has a heavier tail than the exponential distribution.



I will be very glad for any recommendation of an alternative to the exponential distribution for the data.






exponential







share|cite|improve this question











$endgroup$








  • 3




    $begingroup$
    A good basis for any such recommendation is a theory about the underlying process, because tail estimation can be highly uncertain without having a large amount of data. What additional information can you supply about your problem?
    $endgroup$
    – whuber♦
    2 days ago










  • $begingroup$
    @whuber , data is about the time duration(in months) between car accidents day and reporting day of accidents. But I dont have so much data. It seems that, most of the accidents are generally being reported quickly, but some of the accidents are being reported lately. when, I fit the data with an exponantial distribution, I see that the tail seems so light compared with the data.
    $endgroup$
    – oercim
    2 days ago












  • $begingroup$
    One might suppose there is a statute of limitations or insurance limit, most likely a whole number of years. This wouldn't be modeled well by any standard heavy-tailed distribution. You ought to closely examine what data you do have.
    $endgroup$
    – whuber♦
    2 days ago














1












1








1





$begingroup$


I have data whose distribution resembles an exponential distribution, but the data has a heavier tail than the exponential distribution.



I will be very glad for any recommendation of an alternative to the exponential distribution for the data.






exponential







share|cite|improve this question











$endgroup$




I have data whose distribution resembles an exponential distribution, but the data has a heavier tail than the exponential distribution.



I will be very glad for any recommendation of an alternative to the exponential distribution for the data.






exponential




exponential






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Nick Cox

39k587130




39k587130










asked 2 days ago









oercimoercim

284110




284110








  • 3




    $begingroup$
    A good basis for any such recommendation is a theory about the underlying process, because tail estimation can be highly uncertain without having a large amount of data. What additional information can you supply about your problem?
    $endgroup$
    – whuber♦
    2 days ago










  • $begingroup$
    @whuber , data is about the time duration(in months) between car accidents day and reporting day of accidents. But I dont have so much data. It seems that, most of the accidents are generally being reported quickly, but some of the accidents are being reported lately. when, I fit the data with an exponantial distribution, I see that the tail seems so light compared with the data.
    $endgroup$
    – oercim
    2 days ago












  • $begingroup$
    One might suppose there is a statute of limitations or insurance limit, most likely a whole number of years. This wouldn't be modeled well by any standard heavy-tailed distribution. You ought to closely examine what data you do have.
    $endgroup$
    – whuber♦
    2 days ago














  • 3




    $begingroup$
    A good basis for any such recommendation is a theory about the underlying process, because tail estimation can be highly uncertain without having a large amount of data. What additional information can you supply about your problem?
    $endgroup$
    – whuber♦
    2 days ago










  • $begingroup$
    @whuber , data is about the time duration(in months) between car accidents day and reporting day of accidents. But I dont have so much data. It seems that, most of the accidents are generally being reported quickly, but some of the accidents are being reported lately. when, I fit the data with an exponantial distribution, I see that the tail seems so light compared with the data.
    $endgroup$
    – oercim
    2 days ago












  • $begingroup$
    One might suppose there is a statute of limitations or insurance limit, most likely a whole number of years. This wouldn't be modeled well by any standard heavy-tailed distribution. You ought to closely examine what data you do have.
    $endgroup$
    – whuber♦
    2 days ago








3




3




$begingroup$
A good basis for any such recommendation is a theory about the underlying process, because tail estimation can be highly uncertain without having a large amount of data. What additional information can you supply about your problem?
$endgroup$
– whuber♦
2 days ago




$begingroup$
A good basis for any such recommendation is a theory about the underlying process, because tail estimation can be highly uncertain without having a large amount of data. What additional information can you supply about your problem?
$endgroup$
– whuber♦
2 days ago












$begingroup$
@whuber , data is about the time duration(in months) between car accidents day and reporting day of accidents. But I dont have so much data. It seems that, most of the accidents are generally being reported quickly, but some of the accidents are being reported lately. when, I fit the data with an exponantial distribution, I see that the tail seems so light compared with the data.
$endgroup$
– oercim
2 days ago






$begingroup$
@whuber , data is about the time duration(in months) between car accidents day and reporting day of accidents. But I dont have so much data. It seems that, most of the accidents are generally being reported quickly, but some of the accidents are being reported lately. when, I fit the data with an exponantial distribution, I see that the tail seems so light compared with the data.
$endgroup$
– oercim
2 days ago














$begingroup$
One might suppose there is a statute of limitations or insurance limit, most likely a whole number of years. This wouldn't be modeled well by any standard heavy-tailed distribution. You ought to closely examine what data you do have.
$endgroup$
– whuber♦
2 days ago




$begingroup$
One might suppose there is a statute of limitations or insurance limit, most likely a whole number of years. This wouldn't be modeled well by any standard heavy-tailed distribution. You ought to closely examine what data you do have.
$endgroup$
– whuber♦
2 days ago










1 Answer
1






active

oldest

votes


















2












$begingroup$

Given your discussion with @whuber, I would suggest two approaches.



(1) A mixture model, perhaps a mixture of exponentials for simplicity. One can think of these as a heirarchical model, where observations can come from different sub-populations and each sub-population has its own distribution. From what you've described, this sounds like the situation you are looking at; most people who get in an accident report it almost immediately to an insurance provider. Those who wait any significant amount of time are likely following very different patterns.



(2) Kaplan-Meier curves. This is a non-parameteric approach that makes no assumptions about the baseline distributions. This is a very simplified approach that tells you what the data says, not what a constrained model of the data says.



Whether you want to use (1) or (2) depends on your use case; are you interested in knowing the proportion of subjects who don't follow the trend of reporting very quickly? Then (1) answers this question a little more directly (assuming a good fit). Are you just interested in seeing the overall distribution of time to reporting without a model's interpretation of the data? Then use (2).



Also, my advice is that even if you decide to use (1), you should still compare the overall fit with (2) as a form of model checking.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    thanks a lot for the answer. My aim is making some simulations about the duration. I want to generate random data, for the different parameters of the underlying distribution. I guess, (1) seems more adequate for my aim. But,fitting such a distribution(s) may be hard. I will try for it.
    $endgroup$
    – oercim
    2 days ago













Your Answer





StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");

StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "65"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});

function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});


}
});














draft saved

draft discarded


















StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f397893%2falternative-heavy-right-tailed-distribution-to-exponential-distribution%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









2












$begingroup$

Given your discussion with @whuber, I would suggest two approaches.



(1) A mixture model, perhaps a mixture of exponentials for simplicity. One can think of these as a heirarchical model, where observations can come from different sub-populations and each sub-population has its own distribution. From what you've described, this sounds like the situation you are looking at; most people who get in an accident report it almost immediately to an insurance provider. Those who wait any significant amount of time are likely following very different patterns.



(2) Kaplan-Meier curves. This is a non-parameteric approach that makes no assumptions about the baseline distributions. This is a very simplified approach that tells you what the data says, not what a constrained model of the data says.



Whether you want to use (1) or (2) depends on your use case; are you interested in knowing the proportion of subjects who don't follow the trend of reporting very quickly? Then (1) answers this question a little more directly (assuming a good fit). Are you just interested in seeing the overall distribution of time to reporting without a model's interpretation of the data? Then use (2).



Also, my advice is that even if you decide to use (1), you should still compare the overall fit with (2) as a form of model checking.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    thanks a lot for the answer. My aim is making some simulations about the duration. I want to generate random data, for the different parameters of the underlying distribution. I guess, (1) seems more adequate for my aim. But,fitting such a distribution(s) may be hard. I will try for it.
    $endgroup$
    – oercim
    2 days ago


















2












$begingroup$

Given your discussion with @whuber, I would suggest two approaches.



(1) A mixture model, perhaps a mixture of exponentials for simplicity. One can think of these as a heirarchical model, where observations can come from different sub-populations and each sub-population has its own distribution. From what you've described, this sounds like the situation you are looking at; most people who get in an accident report it almost immediately to an insurance provider. Those who wait any significant amount of time are likely following very different patterns.



(2) Kaplan-Meier curves. This is a non-parameteric approach that makes no assumptions about the baseline distributions. This is a very simplified approach that tells you what the data says, not what a constrained model of the data says.



Whether you want to use (1) or (2) depends on your use case; are you interested in knowing the proportion of subjects who don't follow the trend of reporting very quickly? Then (1) answers this question a little more directly (assuming a good fit). Are you just interested in seeing the overall distribution of time to reporting without a model's interpretation of the data? Then use (2).



Also, my advice is that even if you decide to use (1), you should still compare the overall fit with (2) as a form of model checking.






share|cite|improve this answer









$endgroup$













  • $begingroup$
    thanks a lot for the answer. My aim is making some simulations about the duration. I want to generate random data, for the different parameters of the underlying distribution. I guess, (1) seems more adequate for my aim. But,fitting such a distribution(s) may be hard. I will try for it.
    $endgroup$
    – oercim
    2 days ago
















2












2








2





$begingroup$

Given your discussion with @whuber, I would suggest two approaches.



(1) A mixture model, perhaps a mixture of exponentials for simplicity. One can think of these as a heirarchical model, where observations can come from different sub-populations and each sub-population has its own distribution. From what you've described, this sounds like the situation you are looking at; most people who get in an accident report it almost immediately to an insurance provider. Those who wait any significant amount of time are likely following very different patterns.



(2) Kaplan-Meier curves. This is a non-parameteric approach that makes no assumptions about the baseline distributions. This is a very simplified approach that tells you what the data says, not what a constrained model of the data says.



Whether you want to use (1) or (2) depends on your use case; are you interested in knowing the proportion of subjects who don't follow the trend of reporting very quickly? Then (1) answers this question a little more directly (assuming a good fit). Are you just interested in seeing the overall distribution of time to reporting without a model's interpretation of the data? Then use (2).



Also, my advice is that even if you decide to use (1), you should still compare the overall fit with (2) as a form of model checking.






share|cite|improve this answer









$endgroup$



Given your discussion with @whuber, I would suggest two approaches.



(1) A mixture model, perhaps a mixture of exponentials for simplicity. One can think of these as a heirarchical model, where observations can come from different sub-populations and each sub-population has its own distribution. From what you've described, this sounds like the situation you are looking at; most people who get in an accident report it almost immediately to an insurance provider. Those who wait any significant amount of time are likely following very different patterns.



(2) Kaplan-Meier curves. This is a non-parameteric approach that makes no assumptions about the baseline distributions. This is a very simplified approach that tells you what the data says, not what a constrained model of the data says.



Whether you want to use (1) or (2) depends on your use case; are you interested in knowing the proportion of subjects who don't follow the trend of reporting very quickly? Then (1) answers this question a little more directly (assuming a good fit). Are you just interested in seeing the overall distribution of time to reporting without a model's interpretation of the data? Then use (2).



Also, my advice is that even if you decide to use (1), you should still compare the overall fit with (2) as a form of model checking.







share|cite|improve this answer












share|cite|improve this answer



share|cite|improve this answer










answered 2 days ago









Cliff ABCliff AB

13.6k12567




13.6k12567












  • $begingroup$
    thanks a lot for the answer. My aim is making some simulations about the duration. I want to generate random data, for the different parameters of the underlying distribution. I guess, (1) seems more adequate for my aim. But,fitting such a distribution(s) may be hard. I will try for it.
    $endgroup$
    – oercim
    2 days ago




















  • $begingroup$
    thanks a lot for the answer. My aim is making some simulations about the duration. I want to generate random data, for the different parameters of the underlying distribution. I guess, (1) seems more adequate for my aim. But,fitting such a distribution(s) may be hard. I will try for it.
    $endgroup$
    – oercim
    2 days ago


















$begingroup$
thanks a lot for the answer. My aim is making some simulations about the duration. I want to generate random data, for the different parameters of the underlying distribution. I guess, (1) seems more adequate for my aim. But,fitting such a distribution(s) may be hard. I will try for it.
$endgroup$
– oercim
2 days ago






$begingroup$
thanks a lot for the answer. My aim is making some simulations about the duration. I want to generate random data, for the different parameters of the underlying distribution. I guess, (1) seems more adequate for my aim. But,fitting such a distribution(s) may be hard. I will try for it.
$endgroup$
– oercim
2 days ago




















draft saved

draft discarded




















































Thanks for contributing an answer to Cross Validated!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …



  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.


Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fstats.stackexchange.com%2fquestions%2f397893%2falternative-heavy-right-tailed-distribution-to-exponential-distribution%23new-answer', 'question_page');
}
);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

Callistus I

Image
Callistus I Res apud Vicidata repertae: Nativitas : unknown value ; Roma Obitus : 223 ; Roma Pontificatus 217–222 Praecessor : Zephyrinus Successor : Urbanus I Sanctus Callistus qui ieiunium instituit; e libro manu scripto Francogallico saeculo XIV Callistus (natus die ignoto; obiit anno 222), fuit episcopus Romae et Papa Ecclesiae Catholicae Romanae ab anno 217. Vita | Secundum adversarium suum, presbyterem, fuit Hippolytus Callistus, servus argentarii Christiani. Papae Zephyrino, Callistus Romae arcessivit. Callistus fuit primus diaconus ac dux catacumbae apud Viam Appiam, quae hodie Sancti Callisti appellatur. Pontificatus | Nexus externi | Vicimedia Communia plura habent quae ad Callistus I spectant. Fontes Latinae de papis usque ad annum 530 (Papa Felix IV) Liber pontificalis Opera Omnia .mw-parser-output .stipula{padding:3px;background:#F7F8FF;border:1px solid grey;margin:auto}.mw-parser-output .stipula td.cell1{bac...
Read more

Tabula Rosettana

Image
Tabula multilinguis Rosettana in Museo Britannico ostenditur. Tabula Rosettana, [1] etiam titulo OGIS 90 agnita, est stela decreto de rebus sacris in Aegypto anno 196 a.C.n. lato inscripta. Tabula iuxta Rosettam Aegypti, urbem in delta Nili et ad oram maris Mediterranei iacentem, anno 1799 a milite Francico reperta est. Inventio stelae, linguis duabus scripturisque tribus inscriptae, eruditis Instituti Aegypti statim nuntiata est; ibi enim iussu imperatoris Napoleonis eruditi omnium scientiarum (sub aegide Commissionis Scientiarum et Artium) properaverant cum expeditione Francica. Qua a Britannis mox debellata, tabula Rosettana Londinium missa hodie apud Museum Britannicum iacet. Textus Graecus cito lectus interpretationi textuum Aegyptiorum (in formis hieroglyphica et demotica expressorum) gradatim adiuvit. Denique textum plene interpretatus est Ioannes Franciscus Champollion. Ab opere eruditorum cumulativo coepit hodiernus scripturae hieroglyphicae linguaeque Aegyptiae a...
Read more

How to label and detect the document text images

Image
1 $begingroup$ This is what I mean as document text image: I want to label the texts in image as separate blocks and my model should detect these labels as classes. NOTE: This is how the end result should be like: The labels like Block 1, Block 2, Block 3,.. should be Logo, Title, Date,.. Others, etc. Work done: First approach : I tried to implement this method via Object Detection, it didn't work. It didn't even detect any text. Second approach : Then I tried it using PixelLink. As this model is build for scene text detection, it detected each and every text in the image. But this method can detect multiple lines of text if the threshold values are increased. But I have no idea how do I add labels to the text blocks. PIXEL_CLS_WEIGHT_all_ones = 'PIXEL_CLS_WEIGHT_all_ones' PIXEL_C...
Read more