@@ -45,8 +45,8 @@ Multiply the Loss Event Frequency vector by the Loss Magnitude vector
4545 Example
4646~~~~~~~
4747For a given year, if we have the number of times a particular event
48- occurs (Loss Event Frequency/LEF) and the dollar losses associated with
49- each of those events (Loss Magnitude/LM), we can multiply these
48+ occurs (Loss Event Frequency/LEF) and the dollar losses associated with
49+ each of those events (Loss Magnitude/LM), we can multiply these
5050together to derive the ultimate dollar value amount lost (Risk/R).
5151
5252+------------+-----+--------+--------------+
@@ -64,7 +64,7 @@ together to derive the ultimate dollar value amount lost (Risk/R).
6464
6565Description
6666~~~~~~~~~~~
67- A vector of elements which represent the number of times a particular
67+ A vector of elements which represent the number of times a particular
6868loss occurs during a given time frame (generally one year)
6969
7070Restrictions
@@ -119,7 +119,7 @@ multiply these together to derive the number of losses that will occur
119119
120120.. note ::
121121
122- Though intended to represent a discrete number of events, TEF and
122+ Though intended to represent a discrete number of events, TEF and
123123 LEF are not rounded to the nearest integer. This allows for
124124 the modeling of events that happen infrequently. For instance, if
125125 we are running a simulation for a single year, one might model a
@@ -130,7 +130,7 @@ multiply these together to derive the number of losses that will occur
130130
131131Description
132132~~~~~~~~~~~
133- A vector of elements representing the number of times a particular
133+ A vector of elements representing the number of times a particular
134134threat occurs, whether or not it results in a loss
135135
136136Restrictions
@@ -139,7 +139,7 @@ All elements must be positive
139139
140140Derivation
141141~~~~~~~~~~
142- Supplied directly, or multiply the Contact Frequency vector and the
142+ Supplied directly, or multiply the Contact Frequency vector and the
143143Probability of Action vector
144144
145145.. math ::
@@ -312,8 +312,8 @@ a control (Vulnerability/V).
312312
313313Description
314314~~~~~~~~~~~
315- A vector with elements representing the number of threat
316- actor contacts that could potentially yield a threat within a given
315+ A vector with elements representing the number of threat
316+ actor contacts that could potentially yield a threat within a given
317317timeframe
318318
319319Restrictions
@@ -332,7 +332,7 @@ attack, and in turn can potentially yield a loss (Contact Frequency/C).
332332+------------+-----------+
333333| Simulation | C |
334334+============+===========+
335- | 1 | 5,000,000 |
335+ | 1 | 5,000,000 |
336336+------------+-----------+
337337| 2 | 3,000,000 |
338338+------------+-----------+
@@ -345,7 +345,7 @@ attack, and in turn can potentially yield a loss (Contact Frequency/C).
345345Description
346346~~~~~~~~~~~
347347A vector with elements representing the probability that a threat actor
348- will proceed after coming into contact with an organization
348+ will proceed after coming into contact with an organization
349349
350350Restrictions
351351------------
@@ -363,7 +363,7 @@ resource (Probability of Action/P)
363363+------------+------+
364364| Simulation | P |
365365+============+======+
366- | 1 | 0.95 |
366+ | 1 | 0.95 |
367367+------------+------+
368368| 2 | 0.90 |
369369+------------+------+
@@ -375,7 +375,7 @@ resource (Probability of Action/P)
375375
376376Description
377377~~~~~~~~~~~
378- A vector of unitless elements that describe the relative
378+ A vector of unitless elements that describe the relative
379379level of expertise and resources of a threat actor (relative to a
380380Control Strength)
381381
@@ -395,7 +395,7 @@ relates to the relative strength of the controls (Control Strength/CS)
395395+------------+------+
396396| Simulation | TC |
397397+============+======+
398- | 1 | 0.75 |
398+ | 1 | 0.75 |
399399+------------+------+
400400| 2 | 0.60 |
401401+------------+------+
@@ -407,7 +407,7 @@ relates to the relative strength of the controls (Control Strength/CS)
407407
408408Description
409409~~~~~~~~~~~
410- A vector of unitless elements that describe the relative strength of a
410+ A vector of unitless elements that describe the relative strength of a
411411given control (relative to the Threat Capability of a given actor)
412412
413413Restrictions
@@ -427,7 +427,7 @@ Capability/TC)
427427+------------+------+
428428| Simulation | TC |
429429+============+======+
430- | 1 | 0.15 |
430+ | 1 | 0.15 |
431431+------------+------+
432432| 2 | 0.10 |
433433+------------+------+
@@ -514,7 +514,7 @@ Loss/PL)
514514+------------+------------+
515515| Simulation | PL |
516516+============+============+
517- | 1 | $5,000,000 |
517+ | 1 | $5,000,000 |
518518+------------+------------+
519519| 2 | $3,500,000 |
520520+------------+------------+
@@ -540,43 +540,39 @@ multiplied together on an elementwise basis.
540540
541541.. math ::
542542
543- \begin {bmatrix}
544- \text {SL}_{1 } \\
545- \text {SL}_{1 } \\
546- \vdots \\
547- \text {SL}_{1 } \\
548- \end {bmatrix}
549- \quad
550- =
551- \quad
552- \sum \limits ^n_{j=1 }
553- \quad
554- \left (
555- \quad
556- \begin {bmatrix}
557- \text {SLEF}_{1 ,1 } & \text {SLEF}_{1 ,2 } & \dots & \text {SLEF}_{1 ,n} \\
558- \text {SLEF}_{2 ,1 } & \text {SLEF}_{2 ,2 } & \dots & \text {SLEF}_{2 ,n} \\
559- \vdots & \vdots & \ddots & \vdots \\
560- \text {SLEF}_{m,1 } & \text {SLEF}_{m,2 } & \dots & \text {SLEF}_{m,n} \\
561- \end {bmatrix}
562- \quad
563- \circ
564- \quad
565- \begin {bmatrix}
566- \text {SLEM}_{1 ,1 } & \text {SLEM}_{1 ,2 } & \dots & \text {SLEM}_{1 ,n} \\
567- \text {SLEM}_{2 ,1 } & \text {SLEM}_{2 ,2 } & \dots & \text {SLEM}_{2 ,n} \\
568- \vdots & \vdots & \ddots & \vdots \\
569- \text {SLEM}_{m,1 } & \text {SLEM}_{m,2 } & \dots & \text {SLEM}_{m,n} \\
570- \end {bmatrix}
571- \quad
572- \right )
543+ \\ begin{split}
544+ \\ mathbf{SL} &=
545+ \\ sum_{j=1 }^{n} \\ left( \\ mathbf{SLEF} \\ circ \\ mathbf{SLEM} \\ right)_{rowwise} \\\\
546+ \\ text{where:} \\\\
547+ \\ mathbf{SLEF} &=
548+ \\ begin{bmatrix}
549+ \\ text{SLEF}_{1 ,1 } & \\ text{SLEF}_{1 ,2 } & \\ dots & \\ text{SLEF}_{1 ,n} \\\\
550+ \\ text{SLEF}_{2 ,1 } & \\ text{SLEF}_{2 ,2 } & \\ dots & \\ text{SLEF}_{2 ,n} \\\\
551+ \\ vdots & \\ vdots & \\ ddots & \\ vdots \\\\
552+ \\ text{SLEF}_{m,1 } & \\ text{SLEF}_{m,2 } & \\ dots & \\ text{SLEF}_{m,n}
553+ \\ end{bmatrix} \\\\
554+ \\ mathbf{SLEM} &=
555+ \\ begin{bmatrix}
556+ \\ text{SLEM}_{1 ,1 } & \\ text{SLEM}_{1 ,2 } & \\ dots & \\ text{SLEM}_{1 ,n} \\\\
557+ \\ text{SLEM}_{2 ,1 } & \\ text{SLEM}_{2 ,2 } & \\ dots & \\ text{SLEM}_{2 ,n} \\\\
558+ \\ vdots & \\ vdots & \\ ddots & \\ vdots \\\\
559+ \\ text{SLEM}_{m,1 } & \\ text{SLEM}_{m,2 } & \\ dots & \\ text{SLEM}_{m,n}
560+ \\ end{bmatrix} \\\\
561+ \\ mathbf{SL} &=
562+ \\ begin{bmatrix}
563+ \\ text{SL}_{1 } \\\\
564+ \\ text{SL}_{2 } \\\\
565+ \\ vdots \\\\
566+ \\ text{SL}_{m}
567+ \\ end{bmatrix}
568+ \\ end{split}
573569
574570 Example
575571~~~~~~~
576572For a given model, we can have a matrix of secondary loss
577573probabilities. Each row can represent a simulation and each column can
578- represent a loss type. In this example below we have three different
579- probability columns for different types of probability loss. E.g. the
574+ represent a loss type. In this example below we have three different
575+ probability columns for different types of probability loss. E.g. the
580576probabilities of loss for simulation 1 are 0.95, 0.05, and 1.00.
581577
582578+------------+-------------+--------------+--------------+
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